rapidfem 0.4.0

Frequency-domain electromagnetic FEM solver in Rust, with a Python API and an optional local web UI.

RapidFEM

Frequency-domain electromagnetic FEM solver written in Rust, distributed as a Python package on PyPI. Second-kind Nedelec edge elements, complex-symmetric sparse linear algebra, optional Flask-based local UI with a code editor and live geometry viewer.

Install

pip install rapidfem            # solver only
pip install rapidfem[ui]        # solver + local UI

Wheels for Windows, Linux, and macOS are built via CI. The Rust core is compiled ahead of time — no Rust toolchain required on the user's machine.

Gmsh (Python wheel gmsh) is pulled in automatically as a dependency and provides the OpenCASCADE-based geometry + mesher used by rapidfem.Geometry.

Quick start (Python API)

import numpy as np
import rapidfem

# Build geometry with named, tracked entities
g = rapidfem.Geometry()
sub = g.box(60e-3, 60e-3, 1.6e-3, position=(-30e-3, -30e-3, 0))
patch = g.xy_plate(38e-3, 29e-3, position=(-19e-3, -14.5e-3, 1.6e-3))
g.fragment(sub, patch)

sub.faces.min(axis="z").name = "ground"
patch.name = "patch_pec"
sub.material = "fr4"

# Mesh + simulate
mesh_bytes, name_to_tag = g.mesh(maxh=5e-3)
sim = (
    rapidfem.SimulationBuilder()
    .mesh(mesh_bytes, name_to_tag)
    .frequencies(np.linspace(2.3e9, 2.5e9, 21))
    .pec("ground", "patch_pec")
    .lumped_port("feed", direction=(0, 0, 1), z0=50.0)
    .material("fr4", er=4.4)
    .material("air", er=1.0)
    .build()
)

result = sim.run_sweep()
print(result.frequencies.shape, result.sparams.shape)

Local UI

rapidfem serve ./my_project/

Opens a browser window with:

• a CodeMirror Python editor on the left,
• a 3D geometry / mesh / field viewer on the right (raw WebGL2, viridis colormap for scalar fields),
• S-parameter plots in a separate tab,
• a Generate Mesh button (gmsh) and a Run Simulation button (FEM sweep).

The geometry view updates automatically every time you save the file (Ctrl+S). Mesh and solver runs are explicit.

Use rapidfem.show(g) at the bottom of your script to send a geometry to the viewer.

Features

• Nedelec-2 elements — 20 DOFs per tetrahedron, vector edge basis for the curl–curl form of Maxwell's equations
• Excitations — rectangular waveguide ports (arbitrary TE modes), lumped ports (TEM, multi-line voltage integral), and absorbing boundary conditions of order 1 and 2 (selectable coefficient types A–E)
• PML — anisotropic stretched-coordinate perfectly matched layer
• Lossy materials — complex permittivity with loss tangent + conductivity; frequency-independent caching speeds up sweeps
• Sparse solvers — pure-Rust faer LU as the default in the PyPI wheel; optional MKL PARDISO (complex-symmetric LDLᵀ) for the fastest path
• Frequency sweep — assembles E/B once, refactors only the frequency- dependent K per point, reuses the symbolic LU pattern
• Eigenmode solver — shift-invert Lanczos on the complex-symmetric system
• Adaptive refinement — residual error estimator (volume residual + face jumps) with Dörfler marking, exports a size field for gmsh re-meshing
• Output — Touchstone (.s1p/.s2p/.snp), VTK field export, far-field NFFT
• Parallel assembly — rayon-based element matrix evaluation

Solver backends

Solver	Type	Notes
faer	General sparse LU	Pure Rust, no native dependencies — the default in the PyPI wheel
MKL PARDISO	Complex-symmetric LDLᵀ	Fastest path; opt-in, requires mkl_rt on PATH

Choose at simulation time via the builder or with the RAPIDFEM_SOLVER environment variable.

Installing MKL (optional)

• conda: conda install mkl
• pip: pip install mkl
• Intel oneAPI: download

Ensure mkl_rt.dll (or mkl_rt.2.dll) is on the system PATH.

Performance

WR-90 iris waveguide driven sweep, 10 GHz, 2-port:

Mesh	DOFs	PARDISO	faer
693 tets	5 512	0.14 s	0.22 s
1 096 tets	8 382	0.06 s	0.45 s
2 595 tets	19 196	0.17 s	1.39 s
3 284 tets	23 968	0.21 s	1.98 s

Larger problems:

• 327 k DOFs driven sweep (PARDISO): ~5 s per frequency
• 905 k DOFs eigenmode (3-turn spiral, shift-invert Lanczos): ~54 s

Verification

Element-level functions (curl–curl integrals, Robin BC, second-order ABC, mode-power normalization, surface integrals) are checked to machine precision (1e-12 – 1e-16) by cargo test --release.

End-to-end S-parameter accuracy is tracked in tests/validation/ against analytical solutions and external reference solvers.

cargo test --release

License

GNU Affero General Public License v3.0 or later. If you run a modified version of rapidfem as a network service (e.g. SaaS), the AGPL requires that you make the modified source available to the users of that service. For commercial use under different terms, get in touch.