meanas/README.md

# meanas

**meanas** is a python package for electromagnetic simulations

** UNSTABLE / WORK IN PROGRESS **

Formerly known as [fdfd_tools](https://mpxd.net/code/jan/fdfd_tools).

This package is intended for building simulation inputs, analyzing
simulation outputs, and running short simulations on unspecialized hardware.
It is designed to provide tooling and a baseline for other, high-performance
purpose- and hardware-specific solvers.


**Contents**

- Finite difference frequency domain (FDFD)
    * Library of sparse matrices for representing the electromagnetic wave
    equation in 3D, as well as auxiliary matrices for conversion between fields
    * Waveguide mode operators
    * Waveguide mode eigensolver
    * Stretched-coordinate PML boundaries (SCPML)
    * Functional versions of most operators
    * Anisotropic media (limited to diagonal elements eps_xx, eps_yy, eps_zz, mu_xx, ...)
    * Arbitrary distributions of perfect electric and magnetic conductors (PEC / PMC)
- Finite difference time domain (FDTD)
    * Basic Maxwell time-steps
    * Poynting vector and energy calculation
    * Convolutional PMLs

This package does *not* provide a fast matrix solver, though by default
`meanas.fdfd.solvers.generic(...)` will call
`scipy.sparse.linalg.qmr(...)` to perform a solve.
For 2D FDFD problems this should be fine; likewise, the waveguide mode
solver uses scipy's eigenvalue solver, with reasonable results.

For solving large (or 3D) FDFD problems, I recommend a GPU-based iterative
solver, such as [opencl_fdfd](https://mpxd.net/code/jan/opencl_fdfd) or
those included in [MAGMA](http://icl.cs.utk.edu/magma/index.html). Your
solver will need the ability to solve complex symmetric (non-Hermitian)
linear systems, ideally with double precision.

- [Source repository](https://mpxd.net/code/jan/meanas)
- [PyPI](https://pypi.org/project/meanas)
- [Github mirror](https://github.com/anewusername/meanas)


## Installation

**Requirements:**

* python >=3.11
* numpy
* scipy


Install from PyPI with pip:
```bash
pip3 install 'meanas[dev]'
```

### Development install
Install python3 and git:
```bash
# This is for Debian/Ubuntu/other-apt-based systems; you may need an alternative command
sudo apt install python3 build-essential python3-dev git
```

In-place development install:
```bash
# Download using git
git clone https://mpxd.net/code/jan/meanas.git

# If you'd like to create a virtualenv, do so:
python3 -m venv my_venv

# If you are using a virtualenv, activate it
source my_venv/bin/activate

# Install in-place (-e, editable) from ./meanas, including development dependencies ([dev])
pip3 install --user -e './meanas[dev]'

# Run tests
cd meanas
python3 -m pytest -rsxX | tee test_results.txt
```

#### See also:
- [git book](https://git-scm.com/book/en/v2)
- [venv documentation](https://docs.python.org/3/tutorial/venv.html)
- [python language reference](https://docs.python.org/3/reference/index.html)
- [python standard library](https://docs.python.org/3/library/index.html)


## Use

`meanas` is organized around a few core workflows:

- `meanas.fdfd`: frequency-domain wave equations, sparse operators, SCPML, and
  iterative solves for driven problems.
- `meanas.fdfd.waveguide_2d` / `meanas.fdfd.waveguide_3d`: waveguide mode
  solvers, mode-source construction, and overlap windows for port-based
  excitation and analysis.
- `meanas.fdtd`: Yee-step updates, CPML boundaries, flux/energy accounting, and
  on-the-fly phasor extraction for comparing time-domain runs against FDFD.
- `meanas.fdmath`: low-level finite-difference operators, vectorization helpers,
  and derivations shared by the FDTD and FDFD layers.

The most mature user-facing workflows are:

1. Build an FDFD operator or waveguide port source, then solve a driven
   frequency-domain problem.
2. Run an FDTD simulation, extract one or more frequency-domain phasors with
   `meanas.fdtd.accumulate_phasor(...)`, and compare those phasors against an
   FDFD reference on the same Yee grid.

Tracked examples under `examples/` are the intended starting points:

- `examples/fdtd.py`: broadband FDTD pulse excitation, phasor extraction, and a
  residual check against the matching FDFD operator.
- `examples/waveguide.py`: waveguide mode solving, unidirectional mode-source
  construction, overlap readout, and FDTD/FDFD comparison on a guided structure.
- `examples/fdfd.py`: direct frequency-domain waveguide excitation and overlap /
  Poynting analysis without a time-domain run.

Several examples rely on optional packages such as
[gridlock](https://mpxd.net/code/jan/gridlock).

### Frequency-domain waveguide workflow

For a structure with a constant cross-section in one direction:

1. Build `dxes` and the diagonal `epsilon` / `mu` distributions on the Yee grid.
2. Solve the port mode with `meanas.fdfd.waveguide_3d.solve_mode(...)`.
3. Build a unidirectional source with `compute_source(...)`.
4. Build a matching overlap window with `compute_overlap_e(...)`.
5. Solve the full FDFD problem and project the result onto the overlap window or
   evaluate plane flux with `meanas.fdfd.functional.poynting_e_cross_h(...)`.

### Time-domain phasor workflow

For a broadband or continuous-wave FDTD run:

1. Advance the fields with `meanas.fdtd.maxwell_e/maxwell_h` or
   `updates_with_cpml(...)`.
2. Inject electric current using the same sign convention used throughout the
   examples and library: `E -= dt * J / epsilon`.
3. Accumulate the desired phasor with `accumulate_phasor(...)` or the Yee-aware
   wrappers `accumulate_phasor_e/h/j(...)`.
4. Build the matching FDFD operator on the stretched `dxes` if CPML/SCPML is
   part of the simulation, and compare the extracted phasor to the FDFD field or
   residual.