3D Finite-Element Electromagnetics Simulator for RF and mmWave
EdgeFEM is an open-source full-wave FEM solver specialized for metasurface, metamaterial, and phased array unit cell modeling (100 kHz - 110 GHz). It computes S-parameters, electromagnetic fields, and radiation patterns using Nédélec (edge) elements with industry-standard accuracy.
| Feature | Description |
|---|---|
| S-parameters | Wave ports with eigenmode-based extraction (99.4% accuracy) |
| Radiation Patterns | 3D far-field via Stratton-Chu integration |
| Periodic Structures | Floquet ports for infinite array/metasurface analysis |
| Open Boundaries | PML and ABC for antenna/scattering problems |
| Dispersive Materials | Debye, Lorentz, Drude, and DrudeLorentz models |
| Python SDK | Full scriptable API with NumPy integration |
| Design Classes | RectWaveguideDesign, PatchAntennaDesign, UnitCellDesign |
| Plotting Module | 14 publication-quality visualization functions |
| Standard Exports | Touchstone (.sNp), VTK, CSV |
# macOS
brew install cmake ninja eigen gmsh
# Clone and build
git clone https://github.com/jman4162/EdgeFEM.git
cd EdgeFEM
cmake -S . -B build -G Ninja -DCMAKE_BUILD_TYPE=Release -DEDGEFEM_PYTHON=ON
cmake --build build -j
# Set Python path
export PYTHONPATH="$PWD/build/python:$PWD/python:$PYTHONPATH"from edgefem.designs import RectWaveguideDesign
import numpy as np
# Create WR-90 waveguide (X-band)
wg = RectWaveguideDesign(a=22.86e-3, b=10.16e-3, length=50e-3)
wg.generate_mesh(density=10)
# Compute S-parameters at 10 GHz
S = wg.sparams_at_freq(10e9)
print(f"|S11| = {abs(S[0,0]):.4f}") # ~0.001 (matched)
print(f"|S21| = {abs(S[1,0]):.4f}") # ~0.994 (99.4% transmission)from edgefem.designs import PatchAntennaDesign
# 2.4 GHz WiFi patch on FR-4
patch = PatchAntennaDesign(
patch_length=29e-3, patch_width=38e-3,
substrate_height=1.6e-3, substrate_eps_r=4.4
)
patch.set_probe_feed(y_offset=-5e-3)
patch.generate_mesh(density=15)
# Analyze
Z_in = patch.input_impedance(2.4e9)
pattern = patch.radiation_pattern(2.4e9)
D = patch.directivity(2.4e9)
print(f"Directivity: {10*np.log10(D):.1f} dBi")from edgefem.designs import UnitCellDesign
# Periodic unit cell
cell = UnitCellDesign(period_x=5e-3, period_y=5e-3,
substrate_height=0.5e-3, substrate_eps_r=3.5)
cell.add_patch(width=4e-3, length=4e-3)
cell.generate_mesh(density=20)
# Reflection coefficient at normal incidence
R, T = cell.reflection_transmission(10e9, theta=0, phi=0)
Zs = cell.surface_impedance(10e9)- Installation Guide - Build from source
- Quick Start - First simulation in 5 minutes
- API Reference - Complete function documentation
- Tutorials - Jupyter notebook examples
- Validation Report - Accuracy benchmarks
| Tutorial | Description |
|---|---|
| 01_rectangular_waveguide.ipynb | WR-90 S-parameters |
| 02_patch_antenna.ipynb | 2.4 GHz patch design |
| 03_unit_cell.ipynb | Metasurface characterization |
| 04_phased_array.ipynb | Active impedance vs scan |
┌─────────────────────────────────────────────────────────────────┐
│ Python SDK (pyedgefem) │
│ ┌─────────────────────┐ ┌────────────────┐ ┌──────────────┐ │
│ │ Design Classes │ │ Plots Module │ │ Core API │ │
│ │ RectWaveguideDesign │ │ plot_pattern │ │ load_gmsh │ │
│ │ PatchAntennaDesign │ │ plot_sparams │ │ assemble │ │
│ │ UnitCellDesign │ │ plot_coupling │ │ solve │ │
│ └─────────────────────┘ └────────────────┘ └──────────────┘ │
└─────────────────────────────┬───────────────────────────────────┘
│ pybind11
┌─────────────────────────────┴───────────────────────────────────┐
│ C++ Core │
│ ┌──────────┐ ┌──────────┐ ┌────────┐ ┌──────────┐ ┌─────────┐ │
│ │ Mesh │ │ Maxwell │ │ Ports │ │ Solver │ │ Post │ │
│ │ (Gmsh) │ │ Assembly │ │ (Wave/ │ │(BiCGSTAB)│ │ (NTF, │ │
│ │ │ │(PML/ABC) │ │Floquet)│ │ │ │ VTK) │ │
│ └──────────┘ └──────────┘ └────────┘ └──────────┘ └─────────┘ │
└─────────────────────────────────────────────────────────────────┘
EdgeFEM achieves research-grade accuracy:
| Metric | Target | Achieved |
|---|---|---|
| |S21| transmission | > 99% | 99.4% |
| Phase accuracy | < 5° | 1-2° |
| Passivity | |S11|² + |S21|² ≤ 1 | PASS |
| Reciprocity | S12 = S21 | PASS |
See Validation Report for full benchmark results.
EdgeFEM is the full-wave FEM engine in a multi-package RF modeling ecosystem:
┌───────────────────────────────────────────────────────────────┐
│ Application Layer │
│ ┌─────────────────────┐ ┌─────────────────────────────────┐ │
│ │ Phased-Array- │ │ RF Metasurface Package │ │
│ │ Antenna-Model │ │ (planned) │ │
│ └──────────┬──────────┘ └────────────────┬────────────────┘ │
└─────────────┼──────────────────────────────┼──────────────────┘
│ │
▼ ▼
┌─────────────────────────────────────────────────────────────────┐
│ EdgeFEM │
│ Full-wave 3D FEM providing: S-params, patterns, coupling │
└─────────────────────────────────────────────────────────────────┘
- Phased-Array-Antenna-Model: Uses EdgeFEM element patterns and coupling for array synthesis
cmake -S . -B build -G Ninja \
-DCMAKE_BUILD_TYPE=Release \
-DEDGEFEM_PYTHON=ON # Python bindings| Option | Default | Description |
|---|---|---|
EDGEFEM_BUILD_SCALAR |
ON | Scalar Helmholtz solver |
EDGEFEM_BUILD_VECTOR |
ON | Maxwell vector solver |
EDGEFEM_PYTHON |
OFF | Python bindings (pybind11) |
ctest --test-dir build -j # All tests
ctest --test-dir build -L smoke # Quick smoke tests
ctest --test-dir build -L pml # PML absorption testsimport edgefem.plots as vp
# S-parameters vs frequency
vp.plot_sparams_vs_freq(freqs, S_list, params=['S11', 'S21'])
# Radiation patterns
vp.plot_pattern_3d(pattern, interactive=True)
vp.plot_pattern_3d_cuts(pattern, title="E/H-plane")
# Coupling analysis
vp.plot_coupling_matrix(S, title="4×4 Array")
vp.plot_active_impedance_scan(angles, Z_active)| Format | Function | Use Case |
|---|---|---|
| Touchstone (.sNp) | export_touchstone() |
RF circuit simulators |
| VTK (.vtu) | export_fields_vtk() |
ParaView visualization |
| CSV | export_pattern_csv() |
Custom post-processing |
If you use EdgeFEM in your research, please cite:
@software{hodge2026edgefem,
author = {Hodge, John},
title = {{EdgeFEM}: A 3D Finite-Element Electromagnetics Simulator for RF and mmWave},
year = {2026},
month = feb,
version = {1.0.0},
publisher = {GitHub},
url = {https://github.com/jman4162/EdgeFEM},
license = {MIT}
}EdgeFEM v1.0 is optimized for unit cell and metasurface RF modeling. The following features are not yet implemented:
| Feature | Status | Workaround |
|---|---|---|
| Higher-order elements (Tet10) | Planned v1.1 | Use finer mesh |
| Adaptive mesh refinement | Planned v1.1 | Manual mesh refinement in Gmsh |
| Higher-order modes (TE20, TM) | Planned v1.1 | Single-mode analysis only |
| Plane wave excitation | Planned v1.2 | Use Floquet ports for periodic |
| Lumped ports | Planned v1.1 | Use wave ports |
| Anisotropic materials | Not planned | Isotropic only |
| MPI/GPU parallelization | Planned v2.0 | Single-node execution |
| Time-domain solver | Not planned | Frequency-domain only |
For large-scale problems (>5M DOF) or features requiring adaptive refinement, consider commercial tools like HFSS or CST.
- Dispersive materials (Debye, Lorentz, Drude, DrudeLorentz models)
- pip-installable Python package (
pip install edgefem) - GitHub Actions CI/CD with automated wheel builds
- Higher-order waveguide modes (TE20, TE01, TM modes)
- Lumped port excitation
- Higher-order Nédélec elements (Tet10)
- OpenMP parallelization
- Adaptive mesh refinement (h-adaptivity)
- Plane wave excitation for RCS/scattering
- Surface impedance BC (SIBC)
- Direct solver option (MUMPS)
- MPI distributed solving
- GPU acceleration
- Optimization framework
- GUI application
- Use feature branches; PRs require green CI and updated docs
- clang-tidy, formatting, and unit tests are mandatory
- Large features require an ADR (architecture decision record)
See CONTRIBUTING.md for details.
MIT License. See LICENSE for details.
EdgeFEM builds on excellent open-source projects:
