4293 lines
No EOL
166 KiB
HTML
4293 lines
No EOL
166 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="en" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="Electromagnetic simulation tools">
|
||
|
||
|
||
|
||
<link rel="canonical" href="https://mpxd.net/docs/meanas/api/fdtd/">
|
||
|
||
|
||
<link rel="prev" href="../waveguides/">
|
||
|
||
|
||
<link rel="next" href="../fdmath/">
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.6">
|
||
|
||
|
||
|
||
<title>fdtd - meanas</title>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../css/print-site.css">
|
||
|
||
<link rel="stylesheet" href="../../css/print-site-material.css">
|
||
|
||
<link rel="stylesheet" href="../../assets/_mkdocstrings.css">
|
||
|
||
<link rel="stylesheet" href="../../stylesheets/extra.css">
|
||
|
||
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
|
||
|
||
|
||
|
||
|
||
|
||
</head>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<body dir="ltr" data-md-color-scheme="slate" data-md-color-primary="blue-grey" data-md-color-accent="cyan">
|
||
|
||
|
||
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
|
||
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
|
||
<label class="md-overlay" for="__drawer"></label>
|
||
<div data-md-component="skip">
|
||
|
||
|
||
<a href="#fdtd" class="md-skip">
|
||
Skip to content
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<header class="md-header md-header--shadow" data-md-component="header">
|
||
<nav class="md-header__inner md-grid" aria-label="Header">
|
||
<a href="../.." title="meanas" class="md-header__button md-logo" aria-label="meanas" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
<label class="md-header__button md-icon" for="__drawer">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
|
||
</label>
|
||
<div class="md-header__title" data-md-component="header-title">
|
||
<div class="md-header__ellipsis">
|
||
<div class="md-header__topic">
|
||
<span class="md-ellipsis">
|
||
meanas
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
fdtd
|
||
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<form class="md-header__option" data-md-component="palette">
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="blue-grey" data-md-color-accent="cyan" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_0">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5s-1.65.15-2.39.42zM3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29zm.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14zM20.65 7l-1.77 3.79a7.02 7.02 0 0 0-2.38-4.15zm-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29zM12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44z"/></svg>
|
||
</label>
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="teal" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_0" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3zm3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95zm-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31"/></svg>
|
||
</label>
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-header__button md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
</label>
|
||
<div class="md-search" data-md-component="search" role="dialog">
|
||
<label class="md-search__overlay" for="__search"></label>
|
||
<div class="md-search__inner" role="search">
|
||
<form class="md-search__form" name="search">
|
||
<input type="text" class="md-search__input" name="query" aria-label="Search" placeholder="Search" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
|
||
<label class="md-search__icon md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</label>
|
||
<nav class="md-search__options" aria-label="Search">
|
||
|
||
<button type="reset" class="md-search__icon md-icon" title="Clear" aria-label="Clear" tabindex="-1">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
|
||
</button>
|
||
</nav>
|
||
|
||
</form>
|
||
<div class="md-search__output">
|
||
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
|
||
<div class="md-search-result" data-md-component="search-result">
|
||
<div class="md-search-result__meta">
|
||
Initializing search
|
||
</div>
|
||
<ol class="md-search-result__list" role="presentation"></ol>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-header__source">
|
||
<a href="https://mpxd.net/code/jan/meanas" title="Go to repository" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
meanas
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<div class="md-container" data-md-component="container">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<main class="md-main" data-md-component="main">
|
||
<div class="md-main__inner md-grid">
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--primary" aria-label="Navigation" data-md-level="0">
|
||
<label class="md-nav__title" for="__drawer">
|
||
<a href="../.." title="meanas" class="md-nav__button md-logo" aria-label="meanas" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
meanas
|
||
</label>
|
||
|
||
<div class="md-nav__source">
|
||
<a href="https://mpxd.net/code/jan/meanas" title="Go to repository" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
meanas
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../.." class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Home
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" checked>
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../" class="md-nav__link ">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
API
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_2">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
API
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../meanas/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
meanas
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../eigensolvers/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
eigensolvers
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../fdfd/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdfd
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../waveguides/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
waveguides
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdtd
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdtd
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
Table of contents
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> fdtd
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" fdtd">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--timestep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Timestep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--poynting-vector-and-energy-conservation" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Poynting Vector and Energy Conservation
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--sources" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Sources
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--boundary-conditions" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Boundary conditions
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#core-update-and-analysis-helpers" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Core update and analysis helpers
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> base
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" base">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base.maxwell_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> maxwell_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base.maxwell_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> maxwell_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> pml
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" pml">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml.cpml_params" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> cpml_params
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml.updates_with_cpml" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> updates_with_cpml
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.boundaries" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> boundaries
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" boundaries">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.boundaries--todo-conducting-boundary-documentation" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
TODO conducting boundary documentation
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> energy
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" energy">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.poynting" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> poynting
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.poynting_divergence" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> poynting_divergence
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.energy_hstep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> energy_hstep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.energy_estep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> energy_estep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_h2e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_h2e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_e2h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_e2h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.dxmul" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> dxmul
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" phasor">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> temporal_phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor_scale" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> temporal_phasor_scale
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.real_injection_scale" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> real_injection_scale
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../fdmath/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdmath
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
Table of contents
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> fdtd
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" fdtd">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--timestep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Timestep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--poynting-vector-and-energy-conservation" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Poynting Vector and Energy Conservation
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--sources" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Sources
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd--boundary-conditions" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Boundary conditions
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#core-update-and-analysis-helpers" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
Core update and analysis helpers
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> base
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" base">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base.maxwell_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> maxwell_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.base.maxwell_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> maxwell_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> pml
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" pml">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml.cpml_params" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> cpml_params
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.pml.updates_with_cpml" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> updates_with_cpml
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.boundaries" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> boundaries
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" boundaries">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.boundaries--todo-conducting-boundary-documentation" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
TODO conducting boundary documentation
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> energy
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" energy">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.poynting" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> poynting
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.poynting_divergence" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> poynting_divergence
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.energy_hstep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> energy_hstep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.energy_estep" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> energy_estep
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_h2e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_h2e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_e2h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_e2h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.delta_energy_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> delta_energy_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.energy.dxmul" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> dxmul
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" phasor">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> temporal_phasor
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor_scale" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> temporal_phasor_scale
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.real_injection_scale" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> real_injection_scale
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> accumulate_phasor_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_e" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_e
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_h" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_h
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_j" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> reconstruct_real_j
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="fdtd">fdtd<a class="headerlink" href="#fdtd" title="Permanent link">¶</a></h1>
|
||
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd</span>
|
||
|
||
|
||
<a href="#meanas.fdtd" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Utilities for running finite-difference time-domain (FDTD) simulations</p>
|
||
<p>See the discussion of <code>Maxwell's Equations</code> in <code>meanas.fdmath</code> for basic
|
||
mathematical background.</p>
|
||
<h3 id="meanas.fdtd--timestep">Timestep<a class="headerlink" href="#meanas.fdtd--timestep" title="Permanent link">¶</a></h3>
|
||
<p>From the discussion of "Plane waves and the Dispersion relation" in <code>meanas.fdmath</code>,
|
||
we have</p>
|
||
<div class="arithmatex">\[ c^2 \Delta_t^2 = \frac{\Delta_t^2}{\mu \epsilon} < 1/(\frac{1}{\Delta_x^2} + \frac{1}{\Delta_y^2} + \frac{1}{\Delta_z^2}) \]</div>
|
||
|
||
<p>or, if <span class="arithmatex">\(\Delta_x = \Delta_y = \Delta_z\)</span>, then <span class="arithmatex">\(c \Delta_t < \frac{\Delta_x}{\sqrt{3}}\)</span>.</p>
|
||
<p>Based on this, we can set</p>
|
||
<div class="highlight"><pre><span></span><code>dt = sqrt(mu.min() * epsilon.min()) / sqrt(1/dx_min**2 + 1/dy_min**2 + 1/dz_min**2)
|
||
</code></pre></div>
|
||
<p>The <code>dx_min</code>, <code>dy_min</code>, <code>dz_min</code> should be the minimum value across both the base and derived grids.</p>
|
||
<h3 id="meanas.fdtd--poynting-vector-and-energy-conservation">Poynting Vector and Energy Conservation<a class="headerlink" href="#meanas.fdtd--poynting-vector-and-energy-conservation" title="Permanent link">¶</a></h3>
|
||
<p>Let</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
\tilde{S}_{l, l', \vec{r}} &=& &\tilde{E}_{l, \vec{r}} \otimes \hat{H}_{l', \vec{r} + \frac{1}{2}} \\
|
||
&=& &\vec{x} (\tilde{E}^y_{l,m+1,n,p} \hat{H}^z_{l',\vec{r} + \frac{1}{2}} - \tilde{E}^z_{l,m+1,n,p} \hat{H}^y_{l', \vec{r} + \frac{1}{2}}) \\
|
||
& &+ &\vec{y} (\tilde{E}^z_{l,m,n+1,p} \hat{H}^x_{l',\vec{r} + \frac{1}{2}} - \tilde{E}^x_{l,m,n+1,p} \hat{H}^z_{l', \vec{r} + \frac{1}{2}}) \\
|
||
& &+ &\vec{z} (\tilde{E}^x_{l,m,n,p+1} \hat{H}^y_{l',\vec{r} + \frac{1}{2}} - \tilde{E}^y_{l,m,n,p+1} \hat{H}^z_{l', \vec{r} + \frac{1}{2}})
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>where <span class="arithmatex">\(\vec{r} = (m, n, p)\)</span> and <span class="arithmatex">\(\otimes\)</span> is a modified cross product
|
||
in which the <span class="arithmatex">\(\tilde{E}\)</span> terms are shifted as indicated.</p>
|
||
<p>By taking the divergence and rearranging terms, we can show that</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
\hat{\nabla} \cdot \tilde{S}_{l, l', \vec{r}}
|
||
&= \hat{\nabla} \cdot (\tilde{E}_{l, \vec{r}} \otimes \hat{H}_{l', \vec{r} + \frac{1}{2}}) \\
|
||
&= \hat{H}_{l', \vec{r} + \frac{1}{2}} \cdot \tilde{\nabla} \times \tilde{E}_{l, \vec{r}} -
|
||
\tilde{E}_{l, \vec{r}} \cdot \hat{\nabla} \times \hat{H}_{l', \vec{r} + \frac{1}{2}} \\
|
||
&= \hat{H}_{l', \vec{r} + \frac{1}{2}} \cdot
|
||
(-\tilde{\partial}_t \mu_{\vec{r} + \frac{1}{2}} \hat{H}_{l - \frac{1}{2}, \vec{r} + \frac{1}{2}} -
|
||
\hat{M}_{l, \vec{r} + \frac{1}{2}}) -
|
||
\tilde{E}_{l, \vec{r}} \cdot (\hat{\partial}_t \tilde{\epsilon}_{\vec{r}} \tilde{E}_{l'+\frac{1}{2}, \vec{r}} +
|
||
\tilde{J}_{l', \vec{r}}) \\
|
||
&= \hat{H}_{l'} \cdot (-\mu / \Delta_t)(\hat{H}_{l + \frac{1}{2}} - \hat{H}_{l - \frac{1}{2}}) -
|
||
\tilde{E}_l \cdot (\epsilon / \Delta_t )(\tilde{E}_{l'+\frac{1}{2}} - \tilde{E}_{l'-\frac{1}{2}})
|
||
- \hat{H}_{l'} \cdot \hat{M}_{l} - \tilde{E}_l \cdot \tilde{J}_{l'} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>where in the last line the spatial subscripts have been dropped to emphasize
|
||
the time subscripts <span class="arithmatex">\(l, l'\)</span>, i.e.</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
\tilde{E}_l &= \tilde{E}_{l, \vec{r}} \\
|
||
\hat{H}_l &= \tilde{H}_{l, \vec{r} + \frac{1}{2}} \\
|
||
\tilde{\epsilon} &= \tilde{\epsilon}_{\vec{r}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>etc.
|
||
For <span class="arithmatex">\(l' = l + \frac{1}{2}\)</span> we get</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
\hat{\nabla} \cdot \tilde{S}_{l, l + \frac{1}{2}}
|
||
&= \hat{H}_{l + \frac{1}{2}} \cdot
|
||
(-\mu / \Delta_t)(\hat{H}_{l + \frac{1}{2}} - \hat{H}_{l - \frac{1}{2}}) -
|
||
\tilde{E}_l \cdot (\epsilon / \Delta_t)(\tilde{E}_{l+1} - \tilde{E}_l)
|
||
- \hat{H}_{l'} \cdot \hat{M}_l - \tilde{E}_l \cdot \tilde{J}_{l + \frac{1}{2}} \\
|
||
&= (-\mu / \Delta_t)(\hat{H}^2_{l + \frac{1}{2}} - \hat{H}_{l + \frac{1}{2}} \cdot \hat{H}_{l - \frac{1}{2}}) -
|
||
(\epsilon / \Delta_t)(\tilde{E}_{l+1} \cdot \tilde{E}_l - \tilde{E}^2_l)
|
||
- \hat{H}_{l'} \cdot \hat{M}_l - \tilde{E}_l \cdot \tilde{J}_{l + \frac{1}{2}} \\
|
||
&= -(\mu \hat{H}^2_{l + \frac{1}{2}}
|
||
+\epsilon \tilde{E}_{l+1} \cdot \tilde{E}_l) / \Delta_t \\
|
||
+(\mu \hat{H}_{l + \frac{1}{2}} \cdot \hat{H}_{l - \frac{1}{2}}
|
||
+\epsilon \tilde{E}^2_l) / \Delta_t \\
|
||
- \hat{H}_{l+\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l+\frac{1}{2}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>and for <span class="arithmatex">\(l' = l - \frac{1}{2}\)</span>,</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
\hat{\nabla} \cdot \tilde{S}_{l, l - \frac{1}{2}}
|
||
&= (\mu \hat{H}^2_{l - \frac{1}{2}}
|
||
+\epsilon \tilde{E}_{l-1} \cdot \tilde{E}_l) / \Delta_t \\
|
||
-(\mu \hat{H}_{l + \frac{1}{2}} \cdot \hat{H}_{l - \frac{1}{2}}
|
||
+\epsilon \tilde{E}^2_l) / \Delta_t \\
|
||
- \hat{H}_{l-\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l-\frac{1}{2}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>These two results form the discrete time-domain analogue to Poynting's theorem.
|
||
They hint at the expressions for the energy, which can be calculated at the same
|
||
time-index as either the E or H field:</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
U_l &= \epsilon \tilde{E}^2_l + \mu \hat{H}_{l + \frac{1}{2}} \cdot \hat{H}_{l - \frac{1}{2}} \\
|
||
U_{l + \frac{1}{2}} &= \epsilon \tilde{E}_l \cdot \tilde{E}_{l + 1} + \mu \hat{H}^2_{l + \frac{1}{2}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>Rewriting the Poynting theorem in terms of the energy expressions,</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
(U_{l+\frac{1}{2}} - U_l) / \Delta_t
|
||
&= -\hat{\nabla} \cdot \tilde{S}_{l, l + \frac{1}{2}} \\
|
||
- \hat{H}_{l+\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l+\frac{1}{2}} \\
|
||
(U_l - U_{l-\frac{1}{2}}) / \Delta_t
|
||
&= -\hat{\nabla} \cdot \tilde{S}_{l, l - \frac{1}{2}} \\
|
||
- \hat{H}_{l-\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l-\frac{1}{2}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>This result is exact and should practically hold to within numerical precision. No time-
|
||
or spatial-averaging is necessary.</p>
|
||
<p>Note that each value of <span class="arithmatex">\(J\)</span> contributes to the energy twice (i.e. once per field update)
|
||
despite only causing the value of <span class="arithmatex">\(E\)</span> to change once (same for <span class="arithmatex">\(M\)</span> and <span class="arithmatex">\(H\)</span>).</p>
|
||
<h3 id="meanas.fdtd--sources">Sources<a class="headerlink" href="#meanas.fdtd--sources" title="Permanent link">¶</a></h3>
|
||
<p>It is often useful to excite the simulation with an arbitrary broadband pulse and then
|
||
extract the frequency-domain response by performing an on-the-fly Fourier transform
|
||
of the time-domain fields.</p>
|
||
<p><code>accumulate_phasor</code> in <code>meanas.fdtd.phasor</code> performs the phase accumulation for one
|
||
or more target frequencies, while leaving source normalization and simulation-loop
|
||
policy to the caller. <code>temporal_phasor(...)</code> and <code>temporal_phasor_scale(...)</code>
|
||
apply the same Fourier sum to a scalar waveform, which is useful when a pulsed
|
||
source envelope must be normalized before being applied to a point source or
|
||
mode source. <code>real_injection_scale(...)</code> is the corresponding helper for the
|
||
common real-valued injection pattern <code>numpy.real(scale * waveform)</code>. Convenience
|
||
wrappers <code>accumulate_phasor_e</code>, <code>accumulate_phasor_h</code>, and <code>accumulate_phasor_j</code>
|
||
apply the usual Yee time offsets. <code>reconstruct_real(...)</code> and the corresponding
|
||
<code>reconstruct_real_e/h/j(...)</code> wrappers perform the inverse operation, converting
|
||
phasors back into real-valued field snapshots at explicit Yee-aligned times.
|
||
For scalar <code>omega</code>, the reconstruction helpers accept either a plain field
|
||
phasor or the batched <code>(1, *sample_shape)</code> form used by the accumulator helpers.
|
||
The helpers accumulate</p>
|
||
<div class="arithmatex">\[ \Delta_t \sum_l w_l e^{-i \omega t_l} f_l \]</div>
|
||
|
||
<p>with caller-provided sample times and weights. In this codebase the matching
|
||
electric-current convention is typically <code>E -= dt * J / epsilon</code> in FDTD and
|
||
<code>-i \omega J</code> on the right-hand side of the FDFD wave equation.</p>
|
||
<p>For FDTD/FDFD equivalence, this phasor path is the primary comparison workflow.
|
||
It isolates the guided <code>+\omega</code> response that the frequency-domain solver
|
||
targets directly, regardless of whether the underlying FDTD run used real- or
|
||
complex-valued fields.</p>
|
||
<p>For exact pulsed FDTD/FDFD equivalence it is often simplest to keep the
|
||
injected source, fields, and CPML auxiliary state complex-valued. The
|
||
<code>real_injection_scale(...)</code> helper is instead for the more ordinary one-run
|
||
real-valued source path, where the intended positive-frequency waveform is
|
||
injected through <code>numpy.real(scale * waveform)</code> and any remaining negative-
|
||
frequency leakage is controlled by the pulse bandwidth and run length.</p>
|
||
<p><code>reconstruct_real(...)</code> is for a different question: given a phasor, what late
|
||
real-valued field snapshot should it produce? That raw-snapshot comparison is
|
||
stricter and noisier because a monitor plane generally contains both the guided
|
||
field and the remaining orthogonal content,</p>
|
||
<div class="arithmatex">\[ E_{\text{monitor}} = E_{\text{guided}} + E_{\text{residual}} . \]</div>
|
||
|
||
<p>Phasor/modal comparisons mostly validate the guided <code>+\omega</code> term. Raw
|
||
real-field comparisons expose both terms at once, so they should be treated as
|
||
secondary diagnostics rather than the main solver-equivalence benchmark.</p>
|
||
<p>The Ricker wavelet (normalized second derivative of a Gaussian) is commonly used for the pulse
|
||
shape. It can be written</p>
|
||
<div class="arithmatex">\[ f_r(t) = (1 - \frac{1}{2} (\omega (t - \tau))^2) e^{-(\frac{\omega (t - \tau)}{2})^2} \]</div>
|
||
|
||
<p>with <span class="arithmatex">\(\tau > \frac{2 * \pi}{\omega}\)</span> as a minimum delay to avoid a discontinuity at
|
||
t=0 (assuming the source is off for t<0 this gives <span class="arithmatex">\(\sim 10^{-3}\)</span> error at t=0).</p>
|
||
<h3 id="meanas.fdtd--boundary-conditions">Boundary conditions<a class="headerlink" href="#meanas.fdtd--boundary-conditions" title="Permanent link">¶</a></h3>
|
||
<p><code>meanas.fdtd</code> exposes two boundary-related building blocks:</p>
|
||
<ul>
|
||
<li><code>conducting_boundary(...)</code> for simple perfect-electric-conductor style field
|
||
clamping at one face of the domain.</li>
|
||
<li><code>cpml_params(...)</code> and <code>updates_with_cpml(...)</code> for convolutional perfectly
|
||
matched layers (CPMLs) attached to one or more faces of the Yee grid.</li>
|
||
</ul>
|
||
<p><code>updates_with_cpml(...)</code> accepts a three-by-two table of CPML parameter blocks:</p>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a>cpml_params[axis][polarity_index]
|
||
</code></pre></div>
|
||
<p>where <code>axis</code> is <code>0</code>, <code>1</code>, or <code>2</code> and <code>polarity_index</code> corresponds to <code>(-1, +1)</code>.
|
||
Passing <code>None</code> for one entry disables CPML on that face while leaving the other
|
||
directions unchanged. This is how mixed boundary setups such as "absorbing in x,
|
||
periodic in y/z" are expressed.</p>
|
||
<p>When comparing an FDTD run against an FDFD solve, use the same stretched
|
||
coordinate system in both places:</p>
|
||
<ol>
|
||
<li>Build the FDTD update with the desired CPML parameters.</li>
|
||
<li>Stretch the FDFD <code>dxes</code> with the matching SCPML transform.</li>
|
||
<li>Compare the extracted phasor against the FDFD field or residual on those
|
||
stretched <code>dxes</code>.</li>
|
||
</ol>
|
||
<p>The electric-current sign convention used throughout the examples and tests is</p>
|
||
<div class="arithmatex">\[
|
||
E \leftarrow E - \Delta_t J / \epsilon
|
||
\]</div>
|
||
|
||
<p>which matches the FDFD right-hand side</p>
|
||
<div class="arithmatex">\[
|
||
-i \omega J.
|
||
\]</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div><h2 id="core-update-and-analysis-helpers">Core update and analysis helpers<a class="headerlink" href="#core-update-and-analysis-helpers" title="Permanent link">¶</a></h2>
|
||
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd.base" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd.base</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.base" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Basic FDTD field updates</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.base.maxwell_e" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">maxwell_e</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.base.maxwell_e" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">maxwell_e</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_updater_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Build a function which performs a portion the time-domain E-field update,</p>
|
||
<div class="highlight"><pre><span></span><code>E += curl_back(H[t]) / epsilon
|
||
</code></pre></div>
|
||
<p>The full update should be</p>
|
||
<div class="highlight"><pre><span></span><code>E += (curl_back(H[t]) + J) / epsilon
|
||
</code></pre></div>
|
||
<p>which requires an additional step of <code>E += J / epsilon</code> which is not performed
|
||
by the generated function.</p>
|
||
<p>See <code>meanas.fdmath</code> for descriptions of</p>
|
||
<ul>
|
||
<li>This update step: "Maxwell's equations" section</li>
|
||
<li><code>dxes</code>: "Datastructure: dx_lists_t" section</li>
|
||
<li><code>epsilon</code>: "Permittivity and Permeability" section</li>
|
||
</ul>
|
||
<p>Also see the "Timestep" section of <code>meanas.fdtd</code> for a discussion of
|
||
the <code>dt</code> parameter.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dt</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Timestep. See <code>meanas.fdtd</code> for details.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield_updater_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.fdfield_updater_t)" href="../fdmath/#meanas.fdmath.types.fdfield_updater_t">fdfield_updater_t</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Function <code>f(E_old, H_old, epsilon) -> E_new</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.base.maxwell_h" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">maxwell_h</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.base.maxwell_h" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">maxwell_h</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_updater_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Build a function which performs part of the time-domain H-field update,</p>
|
||
<div class="highlight"><pre><span></span><code>H -= curl_forward(E[t]) / mu
|
||
</code></pre></div>
|
||
<p>The full update should be</p>
|
||
<div class="highlight"><pre><span></span><code>H -= (curl_forward(E[t]) + M) / mu
|
||
</code></pre></div>
|
||
<p>which requires an additional step of <code>H -= M / mu</code> which is not performed
|
||
by the generated function; this step can be omitted if there is no magnetic
|
||
current <code>M</code>.</p>
|
||
<p>See <code>meanas.fdmath</code> for descriptions of</p>
|
||
<ul>
|
||
<li>This update step: "Maxwell's equations" section</li>
|
||
<li><code>dxes</code>: "Datastructure: dx_lists_t" section</li>
|
||
<li><code>mu</code>: "Permittivity and Permeability" section</li>
|
||
</ul>
|
||
<p>Also see the "Timestep" section of <code>meanas.fdtd</code> for a discussion of
|
||
the <code>dt</code> parameter.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dt</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Timestep. See <code>meanas.fdtd</code> for details.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield_updater_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.fdfield_updater_t)" href="../fdmath/#meanas.fdmath.types.fdfield_updater_t">fdfield_updater_t</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Function <code>f(E_old, H_old, epsilon) -> E_new</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd.pml" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd.pml</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.pml" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Convolutional perfectly matched layer (CPML) support for FDTD updates.</p>
|
||
<p>The helpers in this module construct per-face CPML parameters and then wrap the
|
||
standard Yee updates with the additional auxiliary <code>psi</code> fields needed by the
|
||
CPML recurrence.</p>
|
||
<p>The intended call pattern is:</p>
|
||
<ol>
|
||
<li>Build a <code>cpml_params[axis][polarity_index]</code> table with <code>cpml_params(...)</code>.</li>
|
||
<li>Pass that table into <code>updates_with_cpml(...)</code> together with <code>dt</code>, <code>dxes</code>, and
|
||
<code>epsilon</code>.</li>
|
||
<li>Advance the returned <code>update_E</code> / <code>update_H</code> closures in the simulation loop.</li>
|
||
</ol>
|
||
<p>Each face can be enabled or disabled independently by replacing one table entry
|
||
with <code>None</code>.</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.pml.cpml_params" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">cpml_params</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.pml.cpml_params" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">cpml_params</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">axis</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">polarity</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">thickness</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">8</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">ln_R_per_layer</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.6</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">epsilon_eff</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">mu_eff</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">m</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">3.5</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">ma</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">cfs_alpha</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="nb">dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">Any</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Construct the parameter block for one CPML face.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>axis</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Which Cartesian axis the CPML is normal to (<code>0</code>, <code>1</code>, or <code>2</code>).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>polarity</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Which face along that axis (<code>-1</code> for the low-index face,
|
||
<code>+1</code> for the high-index face).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dt</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Timestep used by the Yee update.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>thickness</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Number of Yee cells occupied by the CPML region.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>8</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>ln_R_per_layer</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Logarithmic attenuation target per layer.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>-1.6</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon_eff</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Effective permittivity used when choosing the CPML scaling.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>1</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu_eff</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Effective permeability used when choosing the CPML scaling.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>1</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>m</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Polynomial grading exponent for <code>sigma</code> and <code>kappa</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>3.5</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>ma</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Polynomial grading exponent for the complex-frequency shift <code>alpha</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>1</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>cfs_alpha</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Maximum complex-frequency shift parameter.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>0</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="dict">dict</span>[<span title="str">str</span>, <span title="typing.Any">Any</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Dictionary with:</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="dict">dict</span>[<span title="str">str</span>, <span title="typing.Any">Any</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<ul>
|
||
<li><code>param_e</code>: <code>(p0, p1, p2)</code> arrays for the E update</li>
|
||
</ul>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="dict">dict</span>[<span title="str">str</span>, <span title="typing.Any">Any</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<ul>
|
||
<li><code>param_h</code>: <code>(p0, p1, p2)</code> arrays for the H update</li>
|
||
</ul>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="dict">dict</span>[<span title="str">str</span>, <span title="typing.Any">Any</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<ul>
|
||
<li><code>region</code>: slice tuple selecting the CPML cells on that face</li>
|
||
</ul>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.pml.updates_with_cpml" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">updates_with_cpml</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.pml.updates_with_cpml" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">updates_with_cpml</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">cpml_params</span><span class="p">:</span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Sequence</span><span class="p">[</span><span class="nb">dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">Any</span><span class="p">]</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]],</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dtype</span><span class="p">:</span> <span class="n">DTypeLike</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">float32</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">[</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">Callable</span><span class="p">[[</span><span class="n">fdfield_t</span><span class="p">,</span> <span class="n">fdfield_t</span><span class="p">,</span> <span class="n">fdfield_t</span><span class="p">],</span> <span class="kc">None</span><span class="p">],</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">Callable</span><span class="p">[[</span><span class="n">fdfield_t</span><span class="p">,</span> <span class="n">fdfield_t</span><span class="p">,</span> <span class="n">fdfield_t</span><span class="p">],</span> <span class="kc">None</span><span class="p">],</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Build Yee-step update closures augmented with CPML terms.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>cpml_params</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="collections.abc.Sequence">Sequence</span>[<span title="collections.abc.Sequence">Sequence</span>[<span title="dict">dict</span>[<span title="str">str</span>, <span title="typing.Any">Any</span>] | None]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Three-by-two sequence indexed as <code>[axis][polarity_index]</code>.
|
||
Entries are the dictionaries returned by <code>cpml_params(...)</code>; use
|
||
<code>None</code> to disable CPML on one face.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dt</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Timestep.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Yee-grid spacing lists <code>[dx_e, dx_h]</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Electric material distribution used by the E update.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dtype</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="numpy.typing.DTypeLike">DTypeLike</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Storage dtype for the auxiliary CPML state arrays.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code><span title="numpy.float32">float32</span></code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p><code>(update_E, update_H)</code> closures with the same call shape as the basic</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Yee updates:</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="tuple">tuple</span>[<span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None], <span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<ul>
|
||
<li><code>update_E(e, h, epsilon)</code></li>
|
||
</ul>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="tuple">tuple</span>[<span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None], <span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<ul>
|
||
<li><code>update_H(e, h, mu)</code></li>
|
||
</ul>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="tuple">tuple</span>[<span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None], <span title="collections.abc.Callable">Callable</span>[[<span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>, <span title="meanas.fdmath.fdfield_t">fdfield_t</span>], None]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>The closures retain the CPML auxiliary state internally.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd.boundaries" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd.boundaries</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.boundaries" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Boundary conditions</p>
|
||
<h3 id="meanas.fdtd.boundaries--todo-conducting-boundary-documentation">TODO conducting boundary documentation<a class="headerlink" href="#meanas.fdtd.boundaries--todo-conducting-boundary-documentation" title="Permanent link">¶</a></h3>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd.energy" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd.energy</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.poynting" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">poynting</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.poynting" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">poynting</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">e</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Calculate the poynting vector <code>S</code> (<span class="arithmatex">\(S\)</span>).</p>
|
||
<p>This is the energy transfer rate (amount of energy <code>U</code> per <code>dt</code> transferred
|
||
between adjacent cells) in each direction that happens during the half-step
|
||
bounded by the two provided fields.</p>
|
||
<p>The returned vector field <code>S</code> is the energy flow across +x, +y, and +z
|
||
boundaries of the corresponding <code>U</code> cell. For example,</p>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a> mx = numpy.roll(mask, -1, axis=0)
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> my = numpy.roll(mask, -1, axis=1)
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> mz = numpy.roll(mask, -1, axis=2)
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> u_hstep = fdtd.energy_hstep(e0=es[ii - 1], h1=hs[ii], e2=es[ii], **args)
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> u_estep = fdtd.energy_estep(h0=hs[ii], e1=es[ii], h2=hs[ii + 1], **args)
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> delta_j_B = fdtd.delta_energy_j(j0=js[ii], e1=es[ii], dxes=dxes)
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> du_half_h2e = u_estep - u_hstep - delta_j_B
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> s_h2e = -fdtd.poynting(e=es[ii], h=hs[ii], dxes=dxes) * dt
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> planes = [s_h2e[0, mask].sum(), -s_h2e[0, mx].sum(),
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> s_h2e[1, mask].sum(), -s_h2e[1, my].sum(),
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> s_h2e[2, mask].sum(), -s_h2e[2, mz].sum()]
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> assert_close(sum(planes), du_half_h2e[mask])
|
||
</code></pre></div>
|
||
<p>(see <code>meanas.tests.test_fdtd.test_poynting_planes</code>)</p>
|
||
<p>The full relationship is</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
(U_{l+\frac{1}{2}} - U_l) / \Delta_t
|
||
&= -\hat{\nabla} \cdot \tilde{S}_{l, l + \frac{1}{2}} \\
|
||
- \hat{H}_{l+\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l+\frac{1}{2}} \\
|
||
(U_l - U_{l-\frac{1}{2}}) / \Delta_t
|
||
&= -\hat{\nabla} \cdot \tilde{S}_{l, l - \frac{1}{2}} \\
|
||
- \hat{H}_{l-\frac{1}{2}} \cdot \hat{M}_l \\
|
||
- \tilde{E}_l \cdot \tilde{J}_{l-\frac{1}{2}} \\
|
||
\end{aligned}
|
||
\]</div>
|
||
|
||
<p>These equalities are exact and should practically hold to within numerical precision.
|
||
No time- or spatial-averaging is necessary. (See <code>meanas.fdtd</code> docs for derivation.)</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field (one half-timestep before or after <code>e</code>)</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th> <th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td><code>s</code></td> <td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Vector field. Components indicate the energy transfer rate from the
|
||
corresponding energy cell into its +x, +y, and +z neighbors during
|
||
the half-step from the time of the earlier input field until the
|
||
time of later input field.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.poynting_divergence" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">poynting_divergence</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.poynting_divergence" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">poynting_divergence</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">s</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">e</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">h</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Calculate the divergence of the poynting vector.</p>
|
||
<p>This is the net energy flow for each cell, i.e. the change in energy <code>U</code>
|
||
per <code>dt</code> caused by transfer of energy to nearby cells (rather than
|
||
absorption/emission by currents <code>J</code> or <code>M</code>).</p>
|
||
<p>See <code>poynting</code> and <code>meanas.fdtd</code> for more details.
|
||
Args:
|
||
s: Poynting vector, as calculated with <code>poynting</code>. Optional; caller
|
||
can provide <code>e</code> and <code>h</code> instead.
|
||
e: E-field (optional; need either <code>s</code> or both <code>e</code> and <code>h</code>)
|
||
h: H-field (optional; need either <code>s</code> or both <code>e</code> and <code>h</code>)
|
||
dxes: Grid description; see <code>meanas.fdmath</code>.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th> <th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td><code>ds</code></td> <td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Divergence of the poynting vector.
|
||
Entries indicate the net energy flow out of the corresponding
|
||
energy cell.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.energy_hstep" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">energy_hstep</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.energy_hstep" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">energy_hstep</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">e0</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">h1</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">e2</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">mu</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Calculate energy <code>U</code> at the time of the provided H-field <code>h1</code>.</p>
|
||
<p>TODO: Figure out what this means spatially.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e0</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field one half-timestep before the energy.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h1</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field (at the same timestep as the energy).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e2</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field one half-timestep after the energy.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Dielectric constant distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Magnetic permeability distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Energy, at the time of the H-field <code>h1</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.energy_estep" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">energy_estep</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.energy_estep" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">energy_estep</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">h0</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">e1</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">h2</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">mu</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Calculate energy <code>U</code> at the time of the provided E-field <code>e1</code>.</p>
|
||
<p>TODO: Figure out what this means spatially.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h0</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field one half-timestep before the energy.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e1</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field (at the same timestep as the energy).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h2</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field one half-timestep after the energy.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Dielectric constant distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Magnetic permeability distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Energy, at the time of the E-field <code>e1</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.delta_energy_h2e" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">delta_energy_h2e</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.delta_energy_h2e" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">delta_energy_h2e</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">e0</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">h1</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">e2</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">h3</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">mu</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Change in energy during the half-step from <code>h1</code> to <code>e2</code>.</p>
|
||
<p>This is just from (e2 * e2 + h3 * h1) - (h1 * h1 + e0 * e2)</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e0</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field one half-timestep before the start of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h1</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field at the start of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e2</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field at the end of the energy delta (one half-timestep after <code>h1</code>).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h3</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field one half-timestep after the end of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Dielectric constant distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Magnetic permeability distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Change in energy from the time of <code>h1</code> to the time of <code>e2</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.delta_energy_e2h" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">delta_energy_e2h</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.delta_energy_e2h" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">delta_energy_e2h</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">h0</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">e1</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">h2</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">e3</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">mu</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Change in energy during the half-step from <code>e1</code> to <code>h2</code>.</p>
|
||
<p>This is just from (h2 * h2 + e3 * e1) - (e1 * e1 + h0 * h2)</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h0</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field one half-timestep before the start of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e1</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field at the start of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>h2</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>E-field at the end of the energy delta (one half-timestep after <code>e1</code>).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e3</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>H-field one half-timestep after the end of the energy delta.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Dielectric constant distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Magnetic permeability distribution.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; see <code>meanas.fdmath</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Change in energy from the time of <code>e1</code> to the time of <code>h2</code>.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.delta_energy_j" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">delta_energy_j</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.delta_energy_j" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">delta_energy_j</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">j0</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span> <span class="n">e1</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Calculate the electric-current work term <span class="arithmatex">\(J \cdot E\)</span> on the Yee grid.</p>
|
||
<p>This is the source contribution that appears beside the flux divergence in
|
||
the discrete Poynting identities documented in <code>meanas.fdtd</code>.</p>
|
||
<p>Note that each value of <code>J</code> contributes twice in a full Yee cycle (once per
|
||
half-step energy balance) even though it directly changes <code>E</code> only once.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>j0</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Electric-current density sampled at the same half-step as the
|
||
current work term.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>e1</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Electric field sampled at the matching integer timestep.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; defaults to unit spacing.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Per-cell source-work contribution with the scalar field shape.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.energy.dxmul" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">dxmul</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.energy.dxmul" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">dxmul</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">ee</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">hh</span><span class="p">:</span> <span class="n">fdfield</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">epsilon</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="nb">float</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">mu</span><span class="p">:</span> <span class="n">fdfield</span> <span class="o">|</span> <span class="nb">float</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">dxes</span><span class="p">:</span> <span class="n">dx_lists_t</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">)</span> <span class="o">-></span> <span class="n">fdfield_t</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Multiply E- and H-like field products by material weights and cell volumes.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>ee</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Three-component electric-field product, such as <code>e0 * e2</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>hh</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Three-component magnetic-field product, such as <code>h1 * h1</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>epsilon</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | <span title="float">float</span> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Electric material weight; defaults to <code>1</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>mu</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" fdfield (meanas.fdmath.fdfield)" href="../fdmath/#meanas.fdmath.types.fdfield">fdfield</a> | <span title="float">float</span> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Magnetic material weight; defaults to <code>1</code>.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>dxes</code>
|
||
</td>
|
||
<td>
|
||
<code><a class="autorefs autorefs-internal" title=" dx_lists_t
|
||
|
||
|
||
|
||
module-attribute
|
||
(meanas.fdmath.dx_lists_t)" href="../fdmath/#meanas.fdmath.types.dx_lists_t">dx_lists_t</a> | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Grid description; defaults to unit spacing.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Scalar field containing the weighted electric plus magnetic contribution</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="meanas.fdmath.fdfield_t">fdfield_t</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>for each Yee cell.</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.fdtd.phasor" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.fdtd.phasor</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Helpers for extracting single- or multi-frequency phasors from FDTD samples.</p>
|
||
<p>These helpers are intentionally low-level: callers own the accumulator arrays and
|
||
the sampling policy. The accumulated quantity is</p>
|
||
<div class="highlight"><pre><span></span><code>dt * sum(weight * exp(-1j * omega * t_step) * sample_step)
|
||
</code></pre></div>
|
||
<p>where <code>t_step = (step + offset_steps) * dt</code>.</p>
|
||
<p>The usual Yee offsets are:</p>
|
||
<ul>
|
||
<li><code>accumulate_phasor_e(..., step=l)</code> for <code>E_l</code></li>
|
||
<li><code>accumulate_phasor_h(..., step=l)</code> for <code>H_{l + 1/2}</code></li>
|
||
<li><code>accumulate_phasor_j(..., step=l)</code> for <code>J_{l + 1/2}</code></li>
|
||
</ul>
|
||
<p><code>temporal_phasor(...)</code> and <code>temporal_phasor_scale(...)</code> apply the same Fourier
|
||
sum to a 1D scalar waveform. They are useful for normalizing a pulsed source
|
||
before that scalar waveform is applied to a point source or spatial mode source.
|
||
<code>real_injection_scale(...)</code> is a companion helper for the common real-valued
|
||
injection pattern <code>numpy.real(scale * waveform)</code>, where <code>waveform</code> is the
|
||
analytic positive-frequency signal and the injected real current should still
|
||
produce a desired phasor response.
|
||
<code>reconstruct_real(...)</code> and its <code>E/H/J</code> wrappers perform the inverse operation:
|
||
they turn one or more phasors back into real-valued field snapshots at explicit
|
||
Yee-aligned sample times. For a scalar target frequency they accept either a
|
||
plain field phasor or the batched <code>(1, *sample_shape)</code> form used elsewhere in
|
||
this module.</p>
|
||
<p>These helpers do not choose warmup/accumulation windows or pulse-envelope
|
||
normalization. They also do not impose a current sign convention. In this
|
||
codebase, electric-current injection normally appears as <code>E -= dt * J / epsilon</code>,
|
||
which matches the FDFD right-hand side <code>-1j * omega * J</code>.</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.accumulate_phasor" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">accumulate_phasor</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">accumulate_phasor</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">accumulator</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complexfloating</span><span class="p">],</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">sample</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">offset_steps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">weight</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Add one time-domain sample into a phasor accumulator.</p>
|
||
<p>The added quantity is</p>
|
||
<div class="highlight"><pre><span></span><code>dt * weight * exp(-1j * omega * t_step) * sample
|
||
</code></pre></div>
|
||
<p>where <code>t_step = (step + offset_steps) * dt</code>.</p>
|
||
|
||
|
||
<details class="note" open>
|
||
<summary>Note</summary>
|
||
<p>This helper already multiplies by <code>dt</code>. If the caller's normalization
|
||
factor was derived from a discrete sum that already includes <code>dt</code>, pass
|
||
<code>weight / dt</code> here.</p>
|
||
</details>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.temporal_phasor" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">temporal_phasor</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">temporal_phasor</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">samples</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">start_step</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">offset_steps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Fourier-project a 1D temporal waveform onto one or more angular frequencies.</p>
|
||
<p>The returned quantity is</p>
|
||
<div class="highlight"><pre><span></span><code>dt * sum(exp(-1j * omega * t_step) * samples[step_index])
|
||
</code></pre></div>
|
||
<p>where <code>t_step = (start_step + step_index + offset_steps) * dt</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.temporal_phasor_scale" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">temporal_phasor_scale</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.temporal_phasor_scale" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">temporal_phasor_scale</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">samples</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">start_step</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">offset_steps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">target</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Return the scalar multiplier that gives a desired temporal phasor response.</p>
|
||
<p>The returned scale satisfies</p>
|
||
<div class="highlight"><pre><span></span><code>temporal_phasor(scale * samples, omegas, dt, ...) == target
|
||
</code></pre></div>
|
||
<p>for each target frequency. The result keeps a leading frequency axis even
|
||
when <code>omegas</code> is scalar.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.real_injection_scale" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">real_injection_scale</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.real_injection_scale" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">real_injection_scale</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">samples</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">start_step</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">offset_steps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">target</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Return the scale for a real-valued injection built from an analytic waveform.</p>
|
||
<p>If the time-domain source is applied as</p>
|
||
<div class="highlight"><pre><span></span><code>numpy.real(scale * samples[step])
|
||
</code></pre></div>
|
||
<p>then the desired positive-frequency phasor is obtained by compensating for
|
||
the 1/2 factor between the real-valued source and its analytic component:</p>
|
||
<div class="highlight"><pre><span></span><code>scale = 2 * target / temporal_phasor(samples, ...)
|
||
</code></pre></div>
|
||
<p>This helper normalizes only the intended positive-frequency component. Any
|
||
residual negative-frequency leakage is controlled by the waveform design and
|
||
the accumulation window.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.reconstruct_real" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">reconstruct_real</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">reconstruct_real</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">phasors</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">offset_steps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">floating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Reconstruct a real-valued field snapshot from one or more phasors.</p>
|
||
<p>The returned quantity is</p>
|
||
<div class="highlight"><pre><span></span><code>real(phasor * exp(1j * omega * t_step))
|
||
</code></pre></div>
|
||
<p>where <code>t_step = (step + offset_steps) * dt</code>.</p>
|
||
<p>For multi-frequency inputs, the leading frequency axis is preserved. For a
|
||
scalar <code>omega</code>, callers may pass either <code>(1, *sample_shape)</code> or
|
||
<code>sample_shape</code>; the return shape matches that choice.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.accumulate_phasor_e" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">accumulate_phasor_e</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_e" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">accumulate_phasor_e</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">accumulator</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complexfloating</span><span class="p">],</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">sample</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">weight</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Accumulate an E-field sample taken at integer timestep <code>step</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.accumulate_phasor_h" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">accumulate_phasor_h</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_h" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">accumulate_phasor_h</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">accumulator</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complexfloating</span><span class="p">],</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">sample</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">weight</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Accumulate an H-field sample corresponding to <code>H_{step + 1/2}</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.accumulate_phasor_j" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">accumulate_phasor_j</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.accumulate_phasor_j" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">accumulate_phasor_j</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">accumulator</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complexfloating</span><span class="p">],</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">sample</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="o">*</span><span class="p">,</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">weight</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Accumulate a current sample corresponding to <code>J_{step + 1/2}</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.reconstruct_real_e" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">reconstruct_real_e</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_e" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">reconstruct_real_e</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">phasors</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">floating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Reconstruct a real E-field snapshot taken at integer timestep <code>step</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.reconstruct_real_h" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">reconstruct_real_h</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_h" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">reconstruct_real_h</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">phasors</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">floating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Reconstruct a real H-field snapshot corresponding to <code>H_{step + 1/2}</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.fdtd.phasor.reconstruct_real_j" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">reconstruct_real_j</span>
|
||
|
||
|
||
<a href="#meanas.fdtd.phasor.reconstruct_real_j" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">reconstruct_real_j</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">phasors</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">omegas</span><span class="p">:</span> <span class="nb">float</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="o">|</span> <span class="nb">complex</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">float</span> <span class="o">|</span> <span class="nb">complex</span><span class="p">]</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="o">|</span> <span class="n">NDArray</span><span class="p">,</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">dt</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="p">)</span> <span class="o">-></span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">floating</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Reconstruct a real current snapshot corresponding to <code>J_{step + 1/2}</code>.</p>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</article>
|
||
</div>
|
||
|
||
|
||
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
|
||
</div>
|
||
|
||
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
|
||
Back to top
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
<div class="md-footer-meta md-typeset">
|
||
<div class="md-footer-meta__inner md-grid">
|
||
<div class="md-copyright">
|
||
|
||
|
||
Made with
|
||
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
|
||
Material for MkDocs
|
||
</a>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
|
||
</div>
|
||
<div class="md-dialog" data-md-component="dialog">
|
||
<div class="md-dialog__inner md-typeset"></div>
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
<script id="__config" type="application/json">{"annotate": null, "base": "../..", "features": ["navigation.indexes", "navigation.sections", "navigation.top", "content.code.copy", "toc.follow"], "search": "../../assets/javascripts/workers/search.2c215733.min.js", "tags": null, "translations": {"clipboard.copied": "Copied to clipboard", "clipboard.copy": "Copy to clipboard", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.placeholder": "Type to start searching", "search.result.term.missing": "Missing", "select.version": "Select version"}, "version": null}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.79ae519e.min.js"></script>
|
||
|
||
<script src="../../js/print-site.js"></script>
|
||
|
||
<script src="../../javascripts/mathjax.js"></script>
|
||
|
||
<script src="../../assets/vendor/mathjax/startup.js"></script>
|
||
|
||
|
||
</body>
|
||
</html> |