Hertzon

⚠️ 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.

🌐 Website: c8501024.github.io/Hertzon

An open-source 3D full-wave electromagnetic simulator (FEM, frequency domain) for antennas, microwave filters, waveguides, PCB structures and radar cross section, 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).

Hertzon is by Dominik Mair, built on EMerge, the FEM solver by Robert Fennis.

📘 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, your own result quantities with equations, 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. The adaptive mesh refinement (AURA), the error estimate and the curved elements on curved surfaces are EMerge's as well. Hertzon adds the graphical workflow on top: the adaptive pass loop with its convergence criteria, a second local refinement method (hzmesh, local Delaunay), fast and interpolating sweeps with parallel sweep points, far-field and RCS post-processing (also of half and quarter models with symmetry planes), optimization and parametric sweeps, 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.

Install

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.

Updates: when a new version is out, Hertzon shows its release notes in a small dialog after the start (at most once every 7 days) with Install, Skip this version and Later; Help > Check for Updates... checks at any time. Install downloads the installer, checks it and keeps your settings and the Python environment. The check can be switched off in Tools > Options > General, or with HERTZON_NO_UPDATE_CHECK=1.

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

EMerge comes from a pinned commit (see docs/EMERGE_CHANGES.md): prebuilt wheels for Windows x64 and Linux x86_64; on other platforms pip builds it from source, which needs a Rust compiler.

EMerge 3 ships its solver kernels compiled; the first solve only compiles Hertzon's own numba kernels (matrix handling, the size field of the re-mesh refinement), which takes about a minute once; later solves start immediately. On Linux without a desktop, run under xvfb-run.

The workflow

1. Project > Insert Design, then Simulation > Solution Type: Modal, Terminal or Eigenmode, with Auto Open (radiation or PML chosen automatically) or Auto 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 and arcs (3 point, center point), region. Click on the grid (snaps to grid and vertices) or type coordinates in the status bar; every parameter accepts expressions with variables and units. Relative, face and object coordinate systems set the working plane; grid and axes stay at its origin. Modeler > Boolean unite / subtract / intersect / split, arrange, duplicate, thicken, sweep, import STEP; Fillet and Chamfer on the edges of solids or the corner vertices of sheets. A left drag in the 3D view selects everything inside the rectangle; Edit > Group (Ctrl+G) makes objects move, rotate and mirror as one unit, and integration lines follow their objects.
3. Select faces (F) or objects (O) and assign Boundaries (Perfect E/H, Finite Conductivity, Impedance, Lumped RLC, Radiation, PML, Symmetry) and Excitations (Wave Port, Lumped Port, Incident Plane Wave). With Symmetry boundaries a half or quarter model is enough for the far field, which includes the mirror images; a port cut by the plane is still referred to the impedance of the half port (BACKLOG.md). Primary / Secondary (periodic) boundaries make the model a unit cell of an infinite array, with the scan angle on the Secondary boundaries; Floquet ports above and below the cell excite and absorb the plane waves TE00 and TM00. The Lumped Elements tab inserts chip resistors, inductors and capacitors (0201 to 1206 and RF series of Coilcraft and Murata) with a click on the board: pads, element sheet and Lumped RLC boundary with an ideal value, typical ESL/ESR or a Touchstone file of the vendor (docs/LUMPED_ELEMENTS.md).
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, mesh refinement method (hzAURA, EMerge's AURA with exact curved surfaces, by default; local Delaunay or re-mesh). Add Frequency Sweep: discrete, interpolating or fast, linear step / count / log / single points.

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

See docs/TUNING.md for derivative tuning: the workflow, the method (morphed mesh, matrix derivatives, reduced model), its accuracy and limits.

See docs/MESHER.md for how the adaptive mesh refinement works: hzAURA (EMerge's AURA, the default), Hertzon's local Delaunay mesher hzmesh, curved elements and benchmark results.

See docs/BENCHMARKS.md for solve times on a 32-core workstation: a patch antenna with 613k unknowns, swept over a 3:1 band with 101 points, in 203 s (1375 s on one core).

See docs/ROADMAP.md for what comes next: a solver interface for several solvers, openEMS (FDTD), electrostatics and magnetostatics, circuit co-simulation and photonics.

Examples

In Hertzon, File > Open Example opens any of them as an untitled copy, so the shipped files stay unchanged. All of them use the current defaults: hzAURA mesh refinement and curved elements. Most open with their reports and field plots ready: after Analyze All (F5) double-click a report, or right-click a field plot

Animate and Export GIF....

File	What it shows
examples/WaveguidePost.hzn	WR-90 waveguide with an inductive PEC post, wave ports, interpolating sweep 8-12 GHz, Mag E on a cut plane halfway up the guide (tutorial); equations for the return loss, the power through both ports and the power flow along the guide (tutorial)
examples/Microstrip.hzn	50 Ω microstrip on FR4, lumped ports, thin-conductor trace, Auto Open - Filter, sweep 1-6 GHz; second design with a 2.2 pF 0603 DC-block capacitor (Lumped RLC from the Lumped Elements tab, inserted as a group) (tutorial)
examples/PatchAntenna.hzn	2.45 GHz inset-fed patch on FR4, Auto Open (radiation boundary), far field, gain pattern and 3D gain, surface current on the patch and Mag E on a cut plane through the feed
examples/HairpinFilter.hzn	Third-order hairpin band-pass filter at 2.45 GHz on RO4350B, copper losses, sweep 2-2.9 GHz, an optimization and the surface current on the hairpins
examples/GPS_L1_RHCP.hzn	1.575 GHz GPS L1 ceramic patch (εr 20) with probe feed and stub on a feed board, circular polarization (RHCP) far field
examples/RotmanLens_24GHz.hzn	24 GHz Rotman lens beamformer on RO4350B in three designs: the lens with beam, array and dummy ports, the single array patch, and lens plus patch array with beam far fields
examples/PlaneWave.hzn	Incident plane wave on a PEC sphere in a radiation box drawn by hand, and the same plane wave in an empty box
examples/NATO-Sphere.hzn	RCS of a PEC sphere (radius 250 mm) at 1 GHz, plane wave, Auto Open with one wavelength of air, curved second-order elements, Mag E on a drawn plane
examples/DroneRCS.hzn	RCS of an imported drone STL model (Delta_Composites_Demo_3_Layers/) at 1 GHz, plane wave, 3D RCS pattern

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. python examples/make_examples.py builds the first versions of five of them (waveguide, microstrip, patch, hairpin, differential pair) from code; the shipped files were finished in Hertzon.

Manufacturing data (Gerber)

File > Export > Gerber... writes Gerber X2 files per copper layer, the board outline and Excellon drill files (plated / non-plated) from the real CAD geometry: choose the board plane (any coordinate system), origin and units, check the suggested layer assignment in the preview and export. Arcs stay exact, overlapping copper is merged, cut-outs and islands keep their polarity, and simulation helpers (air region, ports, radiation boundaries) are left out. See docs/GERBER_EXPORT.md.

Scripting

• 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.
• Solve on another computer (experimental): a computer in your network runs hertzon-serve (or Tools > Options > Remote > Share this computer) and the laptop pairs with it in Tools > Options > Remote; or Hertzon creates a cloud server for the session in Tools > Options > Cloud (Hetzner Cloud; Amazon Web Services, Google Cloud and Microsoft Azure are marked untested) and deletes it again. Solve on in the status bar switches between this computer, the remote one and the cloud. See docs/REMOTE.md.
• Project files (.hzn) are plain JSON; results go to <project>.hznresults/<design>/<setup>/ (sparams_*.npz, Touchstone *.sNp, fields_*.npz, farfield_*.npz, convergence.json); their layout, units and status values are in docs/RESULT_FILES.md.

AI assistants (MCP)

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)...: press Register next to your assistant (Claude Code gets an entry in ~/.claude.json, the Claude desktop app in claude_desktop_config.json, Codex in ~/.codex/config.toml, VS Code in its user mcp.json). Without the GUI: python -m hertzon.mcp --install claude (or desktop, 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.

Design principles

Hertzon's design principles are in docs/PRINCIPLES.md. The first one: every export is WYSIWYG. Images, animations, plots, reports and data are saved exactly as Hertzon shows them: same size, speed, colours, scales and view.

Layout

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

Changes

What changed in each release: CHANGELOG.md.

Tests

pip install -e ".[test]" && python -m pytest tests

Run the install again whenever packaging/emerge-commit changes: the tests stop with a message when the installed EMerge is not the pinned commit.

Branches and releases

• Work goes to the dev branch (pull requests target dev). Every push to dev builds test installers for Windows and Linux, checks the Windows installation and keeps both as an artifact of the run (Actions tab > Dev build > the run > Artifacts) for 30 days. They are not published as a release.
• For a release, raise the version on dev (pyproject.toml, hertzon/__init__.py, hertzon/mcp/__main__.py, CITATION.cff) and name the section in CHANGELOG.md, then merge dev into main with a merge commit. A new version on main builds the installers and publishes the release v<version>; merges without a new version publish nothing.

Contributors

Thanks to everyone who helps make Hertzon better, whether by reporting a bug, suggesting a feature or writing code. The list follows the all-contributors convention; the emoji key explains the badges.

To add someone, comment on an issue or pull request, for example @all-contributors please add @username for bug (or ideas, code, doc, ...).

Citing Hertzon

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.

License

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.

No warranty

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.