rapidfem 0.10.0

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

RapidFEM

Electromagnetic FEM solver written in Rust, distributed as a Python package on PyPI. Two backends behind one geometry/material/physics API: a frequency-domain solver (second-kind Nedelec edge elements, complex-symmetric sparse linear algebra) and a time-domain DGTD solver (discontinuous Galerkin, Krylov/ETD exponential time integration, model-order reduction). 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 as rf

# Build geometry; attach materials + physics directly to entities
g = rf.Geometry(maxh=rf.lambda_maxh(f_max=12e9))
air = g.box(22.86e-3, 10.16e-3, 30e-3, position=(-11.43e-3, -5.08e-3, 0),
            material=rf.Air())

rf.RectWaveguidePort(air.faces.min(axis="z"))
rf.RectWaveguidePort(air.faces.max(axis="z"))
rf.PEC(*air.faces.unassigned)

g.mesh()

# Define the problem once, run any number of analyses on it
prob = rf.Problem(g)
result = prob.sweep(np.linspace(8e9, 12e9, 21))
print(result.frequencies.shape, result.sparams.shape)

# Same Problem can also drive an eigenmode solve or a far-field pattern:
# modes  = prob.eigenmode(target_frequency=10e9, n_modes=6)
# pattern = prob.farfield(result, freq_idx=10, port_idx=0)

See python_src/rapidfem/examples/ for end-to-end runs of microstrip lines, patch antennas (with PML enclosure + far-field), pyramidal horns, iris filters, dielectric resonators, and more.

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 a no-dependency baseline; optional MKL PARDISO (complex-symmetric LDLᵀ) on Windows / Linux; Apple Accelerate Bunch-Kaufman on macOS (~3× faster than faer)
• 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

Time-domain backend (DGTD)

Alongside the frequency-domain solver, RapidFEM has a time-domain discontinuous-Galerkin (DGTD) backend — ProblemTD, behind the same geometry / material / physics API. Where ProblemFD answers "what are the S-parameters", ProblemTD compiles a structure into an explicit linear ODE dy/dt = A·y and exposes it as a model at every level of abstraction.

• DGTD spatial discretisation — nodal discontinuous Galerkin on tetrahedra, upwind or energy-conserving central flux
• Exponential time integration — matrix-free Krylov/ETD propagator, exact for the linear system at any step size (no CFL limit)
• Model export — the right-hand side, the verbatim sparse operator A, an exponential stepper, or a handoff to an external ODE integrator
• Model-order reduction — Krylov-projected reduced models
• Materials — heterogeneous, lossy, diagonal-anisotropic and Debye dispersive media; matched absorbing layers
• Output — field probes, the RFT transfer function, VTK field-animation export

import rapidfem as rf

ptd  = rf.ProblemTD.box(size=(1, 1, 1), cells=(2, 2, 2), order=2)
traj = ptd.transient(y0, dt=0.02, steps=200)   # turnkey transient
rom  = ptd.reduce(y0, dim=60)                   # model-order reduction
A    = ptd.state_space()                        # the verbatim operator

The time-domain backend is cross-validated against the frequency-domain solver (0.04 % agreement on a shared cavity). Full method notes and the ProblemTD API reference are in docs/td-backend.md.

Solver backends

Solver	Type	Notes
faer	General sparse LU	Pure Rust, no native dependencies — always available
MKL PARDISO	Complex-symmetric LDLᵀ	Fastest path on Windows / Linux; opt-in, requires mkl_rt on PATH
Apple Accelerate	Sparse Bunch-Kaufman LDLᵀ	macOS only; ~3× faster than faer, no extra install (ships with macOS)

Choose at simulation time with the RAPIDFEM_SOLVER environment variable ("auto", "pardiso", "accelerate", "faer") — set before import rapidfem. The default "auto" tries PARDISO → Accelerate → faer in that order, picking the first one that loads.

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.