meanas

meanas is a python package for electromagnetic simulations

** UNSTABLE / WORK IN PROGRESS **

Formerly known as 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 or those included in MAGMA. Your solver will need the ability to solve complex symmetric (non-Hermitian) linear systems, ideally with double precision.

• Source repository
• PyPI
• Github mirror

Installation

Requirements:

• python >=3.11
• numpy
• scipy

Install from PyPI with pip:

pip3 install 'meanas[dev]'

Development install

Install python3 and git:

# 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:

# 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
• venv documentation
• python language reference
• python standard library

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.

Documentation

API and workflow docs are generated from the package docstrings with MkDocs, Material for MkDocs, and mkdocstrings.

Install the docs toolchain with:

pip3 install -e './meanas[docs]'

Then build the docs site with:

./make_docs.sh

This produces:

• a normal multi-page site under site/
• a combined printable single-page HTML site under site/print_page/
• an optional fully inlined site/standalone.html when htmlark is available

The docs build uses a local MathJax bundle vendored under docs/assets/, so the rendered HTML does not rely on external services for equation rendering.

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.

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.