mFES

MATLAB Finite Element Solver for 2D electromagnetic problems.

Solves time-harmonic Maxwell's equations using high-order p-adaptive edge elements (hierarchical curl-conforming basis) on triangular meshes. Supports linear, harmonic balance, and domain decomposition formulations for waveguides, filters, circulators, and scattering structures.

Structure

Directory	Contents
root (.m)	Project scripts — one per application
FEass/	System matrix assembly — linear, harmonic balance, domain decomposition, waveguide ports
FEpre/	Mesh generation, geometry I/O, Triangle wrapper
FEpost/	VTK file output for visualization (ParaView)
Tests/	Unit tests, convergence studies, DD validation, plotting utilities

Requirements

• C/C++ compiler (gcc/g++) — to build the mesh generator
• MATLAB or GNU Octave — to run the solver

Quick start

# Check dependencies and build the mesh generator
./configure
make

% Add paths and set up
Config

% Run a project
ProjectWaveGuide

Workflow

1. Geometry — a .poly file defines the 2D geometry and boundary regions
2. Mesh — IOrPoly() calls IOrMesh which invokes Triangle to generate a triangular mesh, then writes a .mat file with node/element/edge data
3. Solve — the project script assembles the FEM system (mass, stiffness, port matrices), applies BCs, and solves for fields or S-parameters
4. Visualize — results are written to VTK files for viewing in ParaView

The bundled Triangle library handles all mesh generation — no external download needed.

Makefile targets

Target	Description
make / make all	Build IOrMesh and Triangle
make test	Run all tests
make test-<Name>	Run a single test (e.g. make test-TestCoupling)
make project-<Name>	Run a project from MATLAB (e.g. make project-ProjectWaveGuide)
make clean	Remove build artifacts
make install	Copy binaries to FEpre/

Solver capabilities

Feature	Description
Element types	First- and second-order triangular elements (subparametric)
Basis functions	Hierarchical curl-conforming edge elements (p-refinement)
Physics	Time-harmonic Maxwell's equations (E-field, H-field formulations)
BCs	Dirichlet (PEC/PMC), Neumann, impedance, waveguide ports
Domain decomposition	Schur complement-based DD iteration for large problems
Nonlinear	Harmonic balance with Kerr nonlinearity (ferrite circulators, filters)
Output	VTK (ParaView), MATLAB .mat files

Projects

Waveguides

File	Description
ProjectWaveGuide.m	Rectangular waveguide S-parameters
ProjectModalAnalysis.m	TE/TM cutoff frequencies and dispersion
ProjectModalAnalysisOpenStrip.m	Open strip waveguide modes

Filters

File	Description
ProjectBilateralFilter.m	Bilateral fin-line filter S-parameters
ProjectBilateralFilterHB.m	Harmonic balance with Kerr nonlinearity
ProjectBilateralFilterNL.m	Nonlinear bilateral filter
ProjectTwoPostFilter.m	Two-post waveguide filter
ProjectTwoPostFilterHB.m	Two-post filter, harmonic balance
ProjectTwoPostFilterNL.m	Two-post filter, nonlinear

Circulators

File	Description
ProjectCirculator.m	Ferrite circulator full-wave simulation
ProjectCirculatorDDschur.m	Circulator with DD-Schur complement
ProjectCirculatorIMP.m	Circulator intermodulation products
ProjectCirculatorIMP_TestHarmonicConv.m	Circulator IMP harmonic convergence
ProjectCirculatorIMPDDschur.m	Circulator IMP with DD-Schur
ProjectCirculatorIMPDDschur_Acceleration.m	Accelerated circulator IMP-DD-Schur

Scattering

File	Description
ProjectWaveScatteringDD.m	Wave scattering with DD iteration
ProjectWaveScatteringDDglob.m	Wave scattering, DD global formulation
ProjectWaveScatteringEincEs.m	Wave scattering, incident/scattered field split
ProjectWaveScatteringFullField.m	Wave scattering, full-field formulation
ProjectNewDDscattering.m	Domain decomposition scattering (high-order)
ProjectScatteringFloquet.m	Periodic structure scattering with Floquet BCs

Electrostatics & Thermal

File	Description
ProjectElectrostatics.m	Electrostatic potential, Dirichlet BCs
ProjectCapacitiveClearance.m	Capacitive sensor capacitance
ProjectCapacitiveClearanceCorrelated.m	Capacitive sensor with correlated regions
ProjectCableParassitics.m	Coaxial capacitance extraction
ProjectCoaxWideband.m	Coaxial cable wideband capacitance
ProjectThermalDistro.m	Steady-state heat distribution
ProjectThermalDistroDG.m	Transient heat equation, DG in time

Tests

File	Description
fem1ode.m	1D FEM verification (ODE)
TestCoupling.m	Waveguide port coupling verification
TestCouplingGeneric.m	Generic coupling interface test
EntCirc.m	Circular geometry entity helper
ThermalFE.m	Thermal FEM test
TestCurls.m	Curl-conforming basis verification
testGMRES.m	GMRES solver test
TestSurfInteg.m	Surface integration test
TestTetrahedronQuad.m	Tetrahedron quadrature test
TestTetrahedronQuadTraces.m	Trace quadrature test
PlotEfficiency.m	Solver efficiency and memory usage plots
PlotHarmPow.m	Circulator harmonic field results
PlotIMPConv.m	Intermodulation product convergence plots

Domain decomposition tests are in Tests/DD/, nonlinear tests in Tests/NL/.

History

This is a readability-refactored copy of the original FESmat MATLAB code. The git history preserves the original source as the initial commit, followed by mechanical cleanup and a full readability pass (section headers, line breaks, dead code removal, consistent formatting).