Hertzon: Open-Source 3D Full-Wave FEM Solver

Hertzon is under active development. It can still contain bugs, which are being fixed step by step. Please verify important results independently and report problems as GitHub issues.

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An open-source 3D full-wave electromagnetic simulator with a classic engineering workflow: draw the model, assign boundaries and excitations, add an analysis setup with adaptive meshing, add frequency sweeps, analyze, then look at S-parameters, fields and radiation patterns. The finite-element solver underneath is EMerge (2nd-order Nédélec FEM, gmsh/OpenCASCADE geometry).

📘 New to Hertzon? Start with the step-by-step tutorial: a waveguide with wave ports, a coaxial cable, a half-wave dipole and the RCS of a sphere, each from the empty window to the result, plus how to let an AI assistant (Claude Code, Codex, VS Code) build and run simulations for you through Hertzon's MCP server.

Built on EMerge. The finite-element core of Hertzon (Nédélec formulation, element matrices, ports, boundary conditions, solver interface) is EMerge, the open-source FEM solver developed by Robert Fennis. Many thanks to Robert Fennis for making EMerge available under the GPL. Hertzon adds the graphical workflow and its own solver extensions on top: the hzmesh mesher, adaptive refinement (local Delaunay, bisection, Mmg), a fast error estimator, faster assembly kernels, curved elements, far-field and RCS post-processing, and fixes for large models.

Hertzon is a desktop application (Qt + VTK) built for responsiveness with large models: geometry is tessellated incrementally per object, the solver runs in its own process, and results are streamed back into the GUI while it keeps working.

Hertzon is an independent open-source project. It is not affiliated with any vendor of commercial simulation software.

Download the installers from the Releases page.

Windows installer: run Hertzon-Setup-<version>.exe. It installs Hertzon for your user (no administrator rights) into %LOCALAPPDATA%\Programs\Hertzon, adds it to the start menu, the desktop and Settings > Apps (uninstall there), opens .hzn projects with Hertzon and sets up the Python environment (about 1 GB download) before it finishes.

Linux: unpack Hertzon-<version>-linux.tar.gz and run ./install.sh. It installs for your user into ~/.local/share/hertzon, adds Hertzon to the application menu, the command hertzon and the .hzn file type. Run install.sh of a newer package to update, ~/.local/share/hertzon/uninstall.sh to remove it.

Both are built with packaging/build_installer.sh (needs NSIS for the Windows installer); GitHub Actions builds them and publishes a release for every version (.github/workflows/release.yml).

Windows, without installing: unzip and double-click Hertzon.exe. On the first start it installs everything it needs into a .venv folder next to it (Python 3.13 via winget if missing, then EMerge, Qt and VTK, about 1 GB) and compiles the solver with a small test solve, then opens Hertzon. Later starts open Hertzon directly, and the first simulation runs at full speed. You can drag a .hzn file onto Hertzon.exe to open it. To reinstall, delete .venv.

Manually (any OS), Python 3.10 or newer:

python -m venv .venv && source .venv/bin/activate      # Windows: .\setup.ps1 then .\run.ps1
pip install -e .                                        # installs emerge, PySide6, pyvista, pyvistaqt ...
python -m hertzon examples/WaveguidePost.hzn             # or just: hertzon

The first solve compiles EMerge's numba kernels, which takes a few minutes once; later solves start immediately. On Linux without a desktop, run under xvfb-run.

1. Project > Insert Design , thenSimulation > Solution Type : Modal, Terminal or Eigenmode, withAuto Open (radiation or PML chosen automatically) orAuto Open - Filter (air box with fixed margin and a radiation boundary, for filters and other closed-ish circuits).
2. Draw boxes, cylinders, spheres, cones, tori, polyhedra, rectangles, circles, ellipses, polygons, polylines, region. Click on the grid (snaps to grid and vertices) or type coordinates in the status bar; every parameter accepts expressions withvariables and units.Modeler > Boolean unite / subtract / intersect / split, arrange, duplicate, thicken, sweep, import STEP.
3. Select faces (F ) or objects (O ) and assignBoundaries (Perfect E/H, Finite Conductivity, Impedance, Lumped RLC, Radiation, PML, Symmetry) andExcitations (Wave Port, Lumped Port, Floquet Port).
4. Analysis > Add Solution Setup : solution frequency (single / multi / broadband), maximum passes, maximum Delta S, matrix convergence, minimum (converged) passes, percent refinement, maximum refinement, lambda refinement, solver choice.Add Frequency Sweep : discrete or interpolating, linear step / count / log / single points.
5. Validation Check , thenAnalyze All (F5). The progress window shows each adaptive pass;Solution Data shows the convergence table and plot, matrix data and mesh statistics.
6. Results : rectangular plots, Smith chart, data table, radiation pattern, 3D polar plot;Fields : magnitude, complex magnitude and vector plots of E, H and surface current on faces, objects or cut planes, with phase animation. Export Touchstone, CSV, images.

See docs/FEATURE_MATRIX.md for an overview of what is implemented and what is still missing.

See docs/MESHER.md for how the adaptive mesh refinement works: hzmesh, the local Delaunay mesher, curved elements and benchmark results.

examples/benchmark/ holds the validation and timing cases (patch antenna, waveguide post against a reference, sphere RCS against the Mie series, scaling from small to large models) with their scripts. The first four examples are regenerated with python examples/make_examples.py.

• File > Export EMerge Python Script writes a stand-alone script that rebuilds the same EMerge model (geometry, materials, boundaries, ports, initial mesh) and runs the setup, or stops after meshing with--prepare-only so you can continue in plain EMerge.
• Solve without the GUI: python -m hertzon.solver.run Project.hzn DesignName Setup1 out_folder .
• Project files (.hzn ) are plain JSON; results go to<project>.hznresults/<design>/<setup>/ (sparams_*.npz , Touchstone*.sNp ,fields_*.npz ,farfield_*.npz ,convergence.json ).

The tutorial shows the setup and example prompts.

Hertzon ships an MCP server, so Claude Code, Codex or VS Code (Copilot agent mode) can build and run simulations: "build a 2.45 GHz patch on FR4 with a lumped port, solve it and give me S11 and the gain".

1. Tools > AI Assistants (MCP)... : pressRegister next to your assistant (Claude Code gets an entry in~/.claude.json , the Claude desktop app inclaude_desktop_config.json , Codex in~/.codex/config.toml , VS Code in its usermcp.json ). Without the GUI:python -m hertzon.mcp --install claude (ordesktop ,codex ,vscode ,all );python -m hertzon.mcp --config prints the settings for other clients.
2. Tick Let AI assistants work in this window . This also registers Hertzon with every installed Claude Code, Claude desktop app and Codex that does not list it yet. Changes then appear in the open window at once (Ctrl+Z undoes them) and analyses run in its solve queue. Without the live link the assistant works on the.hzn files and runs the solver in the background.
3. Start a new session of the assistant and ask for a simulation.

The server offers tools to create projects, set variables and design settings, draw and import geometry, list faces (index, centre, normal), assign boundaries, ports and mesh operations, define setups, sweeps and far-field spheres, validate, run, follow the adaptive passes, read S-parameters, gain or RCS, and render a picture of the model.

The Python package keeps its short name hertzon, and projects keep the .hzn extension.

hertzon/model    data model, expressions with units, materials, property schema, validation
hertzon/kernel   OpenCASCADE (gmsh) geometry builder and display tessellation
hertzon/solver   EMerge bridge: auto open, boundary mapping, adaptive passes, sweeps, far field
hertzon/gui      main window, 3D modeler, project tree, property grids, reports, field overlays
hertzon/mcp      MCP server for AI assistants, live link to the window, client registration
pip install pytest && python -m pytest tests

If you use Hertzon in a publication, please cite it. GitHub shows a ready-made reference under Cite this repository on the repository page (from CITATION.cff), as APA or BibTeX. Every release is archived on Zenodo with its own DOI; the badge at the top links to the latest one. Please also cite EMerge by Robert Fennis, the solver Hertzon is built on: DOI 10.5281/zenodo.17025518.

GPL-2.0-or-later, the same as EMerge, which Hertzon links against. All Python packages Hertzon uses and their licences are listed in docs/THIRD_PARTY.md.

Hertzon is provided "as is", without any warranty and without liability for damages, as set out in sections 11 and 12 of the GPL. Simulation results can be wrong. Check them yourself (measurements, analytical estimates or a second tool) before you rely on them for a design, a product or a decision.