Radia

Electromagnetic CAE you can operate through AI and MCP
Connect CAD, mesh control, field analysis, and result inspection on NGSolve, through the Python CPU API and MCP tools.

_{Design for a field target: a stream-function active-shield demonstration. This comparison is for the illustrated coil configuration, not a universal shielding-performance claim.}

You set the analysis direction. AI helps operate the CAE tools.

Radia is an open-source electromagnetic CAE platform that an AI assistant can operate through MCP. Specify the analysis task and conditions; connected tools can prepare geometry, control meshing, execute supported calculations, and inspect results. This reduces the need to memorize each tool's commands and interaction sequences while keeping the model and results inspectable.

Start with radia for CPU calculations in Python and radia-mcp for AI-assisted tool operation. The CPU solver builds on NGSolve and does not require MATLAB.

MATLAB GPU development and other independently released packages are described under Related distributions.

Start from supported CAD, mesh, or model data where available, instead of rebuilding every input. What transfers depends on the format and workflow; materials, sources, boundary conditions, and units still need to be checked. The user defines the physical assumptions, analysis plan, and acceptance criteria and evaluates the engineering conclusions. Radia's current positioning is AI-operable CAE, not autonomous design decision-making.

Radia is deliberately not another monolithic finite-element solver. It is built on NGSolve, which remains the numerical foundation for finite-element spaces, mappings, quadrature, weak forms, assembly, and field evaluation. Radia adds electromagnetic methods, open-boundary operators, application workflows, native kernels, and orchestration around that foundation.

Radia extends NGSolve; it does not compete with it.

Python capabilities | Quick start | Analysis with MCP | Related distributions | Eqnedit64 | Documentation | Contributing

Find your next engineering workflow

Use the documentation to discover capabilities and inspect results. Carry out CPU analysis through Python or MCP, using checked CAD and mesh artifacts. Human–AI collaboration through Cubit and supported MATLAB/Simulink workflows is also available; MATLAB/Simulink belongs to the independent radia-simulink package. The executable samples live in tests/ for small usage and contract examples, and validation_test/ for physics and application cases with numerical evidence.

Start here · Result gallery · Accuracy and validation

What you can do in Python

Use Radia to calculate magnetic fields, study material and conductor response, and build field-design loops on a CPU. Start with a small analytical model, or use NGSolve when the problem needs a mesh and finite-element formulation.

The analytical magnet example below is the shortest starting point. Other families have their own mesh, material, dependency and validation requirements; the linked guides and MCP tools describe those prerequisites. HDiv-MMM topology optimization remains an active development and validation priority.

Open boundaries and inspectable results are central to Radia. Analytical sources and integral/open-boundary methods can avoid a large surrounding air mesh where the chosen formulation permits it. NGSolve owns finite-element spaces and assembly; Radia adds electromagnetic formulations and coupling. Use independent references and convergence studies to judge a result for your model. A solver residual alone does not establish physical accuracy.

Quick start

The current production wheel targets Windows x64, Python 3.12, and NGSolve/Netgen 6.2.2607.

python -m pip install --upgrade radia

Evaluate an analytical open-boundary magnetic field in SI units:

import numpy as np
import radia as rad

mu0 = 4.0 * np.pi * 1e-7
remanence_t = 1.2

magnet = rad.ObjRecMag(
    [0.0, 0.0, 0.0],
    [0.01, 0.01, 0.01],
    [0.0, 0.0, remanence_t / mu0],
)

b_t = rad.Fld(magnet, "b", [0.0, 0.0, 0.02])
print(f"Bz [T] = {b_t[2]:.8f}")
rad.UtiDelAll()

Bz [T] = 0.02356629

This first example needs no air mesh. Move to NGSolve when the problem needs finite-element spaces, material domains, weak forms, or coupled field equations.

Turn solved SI field samples into electromagnetic force and torque through Lorentz volume integration, air-side Maxwell stress, time-averaged complex phasors, virtual work/coenergy, or a cylindrical air-gap shear estimate:

from radia.force import integrate_lorentz_force

# One quadrature sample: J = 2 MA/m^2 in +z, B = 0.3 T in +y,
# with 2.5 cm^3 of physical volume. The force points in -x.
force_n = integrate_lorentz_force(
    [0.0, 0.0, 2.0e6],
    [0.0, 0.3, 0.0],
    2.5e-6,
)
print(force_n)  # [-1.5, 0.0, 0.0] N

Supplying quadrature positions and a pivot to integrate_lorentz_force_and_torque returns both resultants. The force and torque validation corpus records the Lorentz, Maxwell-stress, and virtual-work checks used to verify signs and force extraction before attaching them to a production field solve.

Install only the integrations you need:

# AI-facing domain tools and executable workflow knowledge
python -m pip install radia-mcp

# Coreform Cubit export and strict .vol checking
python -m pip install "radia[cubit]"
cubit-plugin-install
cubit-plugin-install --verify-only

# Optional accelerator tracking and topology-to-CAD workflows
python -m pip install "radia[beam]"
python -m pip install "radia[topopt-cad]"

See Installation for package requirements and source builds.

Interfaces

Python and MCP

Python exposes the CPU calculations. MCP (Model Context Protocol) connects an AI assistant to tools that can inspect inputs, prepare models, run supported calculations, and inspect results. Install the solver for numerical execution and the MCP package for the assistant's tool interface:

python -m pip install radia radia-mcp

Then register the required servers in your MCP client; installation alone does not connect them. See client configuration and capability packs. Connect only the domains needed for the task. Cubit operation uses the independently installed cubit-mesh-export server and a licensed Cubit installation.

For example, you can ask an assistant:

Analyze the on-axis magnetic field of a circular coil in air. Use a radius of 50 mm, 100 turns and 1 A DC. Evaluate Bz from -100 mm to +100 mm on the axis. State the conductor approximation and compare the result with the analytical circular-loop field. Report the error and save the inputs, plot and results.

This is an example analysis request, not a record of an executed run. The assistant should establish the supported coil representation and comparison criteria before calculating. A finite-section winding and an ideal filament are different physical models.

The simple analytical example needs no mesh. Mesh-based workflows pass their solver-bound .vol through check-vol with the required label contract. AI operation of Cubit is headless; journals, checkpoints and exported artifacts support inspection and handoff.

For capability packs, start with capability_pack_status; follow the domain status and usage tools it reports. The checked radia_mcp.meta catalog provides discovery metadata and each connected server's live tools/list gives its available tools. Tools may return guidance or prepare scripts as well as execute calculations: inspect their contract and returned artifacts rather than assuming every operation performs a solve.

You define the analysis purpose, physical assumptions and acceptance criteria, and judge the engineering conclusion. MCP supplies the current operating guidance and tool contracts; this README and the saved documentation examples introduce capabilities. Knowledge tools can work without the native solver, but numerical execution requires the selected backend and its dependencies. Unsupported inputs or unavailable backends must be resolved explicitly.

Architecture

flowchart TB
    AI["AI / LLM"] --> MCP["radia-mcp"]
    Human["Human engineer"] --> Python
    Human --> Simulink["MATLAB / Simulink<br/>radia-simulink: separately validated workflows"]
    Simulink --> GPU["radia-simulink MATLAB / mexcuda kernels"]
    GPU --> Results
    Python["Python API"] --> Contract["DesignSpec + typed artifacts"]
    MCP --> Contract

    Contract --> CAD["CAD and mesh<br/>build123d | Cubit | Netgen"]
    Contract --> Methods["Radia physical methods<br/>Hodograph | VIM | Eddy | PEEC | Stream Function"]
    CAD --> NGSolve["NGSolve / ngsolve.bem<br/>spaces | mappings | quadrature | assembly"]
    NGSolve <--> Methods

    Methods --> Native["CPU C++ / pybind11<br/>HACApK | sparse solvers | reduced state"]
    Methods --> Results["Durable results<br/>result.json | run.log | .msh | notebooks"]
    Native --> Results
    Results --> Viz["WebGUI | Gmsh | plots | animation"]

Supported CPU workflows can be driven by a Python program or an AI assistant through MCP. The physical model and numerical checks remain explicit.

Responsibility boundaries

Capabilities

Executed feature notebooks

These existing notebooks contain saved code outputs. Their linked derivations and validation records define the evidence scope; saved output is not a new release acceptance run.

Analytical and open-boundary magnetics

Radia retains the analytical magnetostatic strengths of the original Radia project: permanent magnets, coils, source fields, forces, energies, and field evaluation in open space. Around those sources, the current platform provides Kelvin transformations, exterior DtN formulations, infinite elements, equivalent sources, and integral formulations for problems where truncating a large air domain is undesirable.

Radia targets the magneto-quasi-static to Darwin regime. Its propagation kernels are Laplace kernels; frequency enters conductor physics through skin depth, impedance, and reduced dynamics. Radia is not a full-wave Helmholtz solver for radiation-dominated problems.

Clebsch-Hodograph design

Hodograph methods transform selected nonlinear magnetic-design problems into tractable design problems in a transformed coordinate space. The implementation supports flux-line and pole-face design, field-quality studies, end effects, and accelerator-magnet workflows.

• Clebsch-Hodograph documentation
• Result-bearing accelerator design notebooks

HDiv-MMM topology optimization and magnetic materials

HDiv-MMM (the HDiv magnetic-moment method) is the priority development route for material topology optimization. Its density adjoints, constrained design loops and exact-void checks are demonstrated on verification-scale models; these do not establish engineering-scale optimization acceptance.

The HDiv Volume Integral Method uses NGSolve meshes and finite-element spaces while Radia supplies the magnetic charge-Gram and open-boundary interaction. The C++ HACApK path provides compressed operators for large repeated actions, and the Python surface uses NGSolve's field and space vocabulary.

This is Radia's forward path for soft magnetic materials, nonlinear magnetization, demagnetizing fields, topology-aware material design, and independent FEM/integral cross-checks.

• HDiv-VIM documentation
• Open-boundary method map

Eddy currents, SIBC, and ESIM

Radia combines high-order NGSolve HCurl discretizations with BEM-A, surface impedance, effective surface impedance, cohomology handling, and reduced models. The Eddyable concept packages response bases for repeated low-frequency solves while preserving the underlying field formulation.

• Eddy-current method guide
• ESIM formulation and usage
• Foster, PRIMA, and Modal-bulk SIBC models

Stream functions and coil topology

The stream-function layer solves inverse source problems for target magnetic fields, supports regularized ACA+ / TSVD compression, extracts current contours, and turns them into connected winding paths. It is used for planar, cylindrical, and free-form current sheets as well as field-shaping and coil optimization.

• Stream Function documentation
• Single-stroke winding policy and algorithms

PEEC, circuits, and model reduction

PEEC workflows cover partial inductance, resistance, proximity and skin effects, shield coupling, circuit assembly, and SPICE-compatible extraction. PRIMA, block Lanczos, Foster modal models, and universal relaxation networks provide reusable reduced models for circuit and transient studies.

LTspice and MATLAB/Simulink integration belong to the separate radia-simulink distribution.

• PEEC integration
• SPICE and LTspice integration
• Universal relaxation networks

Optimization and geometry regeneration

Radia supports global, local, and gradient-based design loops:

• TPE, CMA-ES, GP, NSGA-II/III, QMC, and finite define-by-run search;
• analytic-adjoint MMA and SQP for continuous field optimization;
• HDiv-VIM and HCurl material topology;
• stream-function, sheet-metal, and electromagnet topology optimization;
• density/level-set to watertight STL and checked Cubit/Netgen mesh regeneration.

Optimization is tied to the same mesh, material, result, and provenance contracts as direct analysis. A new geometry is not accepted merely because an optimizer produced it.

Accelerator fields and particle trajectories

Radia's C++ core provides inspectable SI field sampling, relativistic Lorentz equations, RK4/Boris steps, fixed-step trajectories, and distributed R/T/U transfer attribution. It can also hand solved magnetic fields to CERN Xsuite for accelerator-coordinate tracking or use SciPy for adaptive trajectories, event handling, and closed-orbit workflows. Gmsh exports preserve trajectory quantities and can animate a beam through the solved field.

For high-order map analysis, NGSolve remains the source of truth for conforming HCurl/HDiv projection and curved finite-element evaluation. Radia adds a tracking-specialized CanonicalHCurl vacuum chain fitted from full-volume field samples, with adaptive fringe grading, periodic ring closure, and direct longitudinal-polynomial coupling to a nonautonomous fourth-order Lie-map integrator. Independent canonical A-map and projected B-map Runge--Kutta routes keep field-projection error separate from Lie truncation error.

• Executed particle-orbit notebook
• Native beam and transfer API design
• Canonical HCurl and Lie-map validation
• Gmsh post-processing guide

Related tools and documentation

Related distributions

This monorepo independently releases radia, radia-mcp, cubit-mesh-export, radia-simulink, radia-optuna, and eqnedit64.

CPU execution belongs to radia through Python/pybind11 and NGSolve. GPU kernels belong to radia-simulink, are compiled with MATLAB mexcuda, and may be called from MATLAB or Python within each validated route.

radia-simulink owns MATLAB, Simulink, LTspice integration, and MATLAB mexcuda development. GPU support is under development; consult that package for validated capabilities. It does not yet provide a GPU equivalent of the full Python CPU feature set. An explicitly selected CPU route compiled with mexcuda is permitted after API tracing proves that it creates no CUDA context, with and without a device. There is no separate CPU-only MEX build. CPU and GPU selection is explicit, with no implicit fallback. Python CPU accuracy checks remain independent of the shared CUDA kernels and are not a GPU-user prerequisite. The GPU toolchain uses MATLAB-bundled CUDA 12.8 and Visual Studio Build Tools 2022 / MSVC 14.44; see the package guide for build and validation requirements.

radia-optuna independently owns MATLAB optimization workflows. Eqnedit64 is the independent equation editor. These packages are separate from installing and using the Python CPU solver.

Eqnedit64

Eqnedit64 is an independently released Windows equation editor with a browser edition and Python API. It connects structural input to UTF-8 TeX and editable Office Math or image export. See the 3.1.4 release and package documentation.

Documentation and visualization

docs/**/*.ipynb is the feature-introduction layer. Demonstrations are executed notebooks with narrative, code, saved results, and saved ngsolve.webgui.Draw or netgen.webgui.Draw scenes. They are not hidden production workbenches. Executable samples live in tests/ and validation_test/. Benchmarks and numerical evidence live under validation_test/ with machine-readable JSON; docs notebooks need no sidecar.

Field-producing application runs write checked Gmsh .msh v4.1 artifacts. The Gmsh toolchain supports scalar/vector/tensor fields, sections, clipping, isosurfaces, LIC, streamlines, file-series statistics, shared-camera comparisons, and particle-track animation. Geometry is shown at physical 1:1:1 axis scale unless an explicit display exaggeration is recorded.

Engineering contracts

Radia favors fail-loud, inspectable boundaries over convenient ambiguity.

For Cubit-to-NGSolve workflows, Cubit produces the mesh and Radia/NGSolve consumes it. The exporter does not infer material constants from labels; conductivity, permeability, BH data, frequency, and other physics remain explicit configuration.

Installation

Supported production stack

Python packages

This monorepo contains six independently versioned distributions. MATLAB, Simulink and LTspice integration belongs to radia-simulink, including its Python circuit-conversion and parser modules.

Each distribution has its own release and validation gates. Record exact package versions when reproducing a calculation. See the GitHub Releases page for artifacts and release notes; the source version above is not a claim of a stable GPU release.

Build from source

git clone https://github.com/ksugahar/Radia.git
Set-Location Radia
python -m pip install -e ".[dev]"
python -m pip install -e packages/radia-mcp
python -m pip install -e packages/cubit-mesh-export
python -m pip install packages/eqnedit64
pwsh -NoProfile -ExecutionPolicy Bypass -File .\Build.ps1 -RadiaOnly

See BUILD.md for compiler, NGSolve, MKL, and packaging details.

Repository map

src/core/                       C++ Radia and native electromagnetic kernels
src/radia/                      CPU Python package and NGSolve integration
packages/radia-simulink/             CUDA MEX, MATLAB, Simulink and LTspice integration
packages/radia-mcp/             MCP servers and executable domain knowledge
packages/cubit-mesh-export/     Cubit exporters, plugin and check-vol
packages/radia-optuna/          Independent MATLAB/Simulink Optuna package
packages/eqnedit64/             Windows Eqnedit64 Python/API distribution
tools/eqnedit64/                Native and browser equation editor source
tests/                          Small executable samples and fast regressions
validation_test/                Physics/application samples and validation gates
docs/                           Feature introductions, saved results and theory
tools/                          Build, policy, release and verification tools

Loose examples/ scripts are retired. New experiments begin outside the repository and are promoted only when they become a reusable API, focused test, validation problem, or result-bearing docs notebook.

Documentation

Start with the path closest to your task:

• Documentation index
• Python API reference
• Radia and NGSolve integration notebook
• Analytical electromagnetic formulas
• HDiv-VIM
• Clebsch-Hodograph
• Eddy-current methods
• Stream Function
• PEEC integration
• Induction heating
• Electric machines
• Magnetic levitation
• Gmsh post-processing
• MATLAB and Simulink
• MCP servers and tools
• Cubit mesh export

Contributing

Radia welcomes focused contributions to physical methods, NGSolve-native integration, independent validation, CAD/mesh boundaries, CPU numerical checks, documentation, and application workflows.

# Run one focused regression while developing
python -m pytest -q tests/test_vim_eddy_hybrid.py

# Broaden only after the focused lane is green
python -m pytest -q tests

Fast regressions belong in tests/. Long numerical studies, convergence sweeps, and benchmark-quality checks belong in validation_test/. These two directories also provide executable samples. Feature introductions and saved demonstrations belong under docs/; operational workflows use MCP or human–AI collaboration through Cubit and Simulink. MATLAB/Simulink workflows belong to their independently validated distributions.

• Read CONTRIBUTING.md before opening a pull request.
• Use the issue tracker for bugs and concrete feature requests.
• Report vulnerabilities through the private process in SECURITY.md.
• Include the smallest reproducible geometry/configuration and the generated result.json or checker report when reporting a numerical workflow issue.

If Radia is useful to your engineering or research, star the repository. It helps other electromagnetic developers discover the project and follow its progress.

Project status

Radia is an active research and engineering platform. The core analytical magnetostatics package is mature; newer VIM, Eddy, and optimization families are developed behind explicit tests and release gates. Not every method has the same maturity or platform coverage, and unsupported paths are expected to fail loudly rather than select a weaker substitute.

Current priorities are:

1. complete and validate HDiv-MMM topology optimization;
2. improve repository and MCP quality, maintenance, validation, builds, CI, packaging, and release operation.

Heritage, acknowledgements, and license

Radia originates from the magnetostatics work developed by Oleg Chubar, Pascal Elleaume, and collaborators at the European Synchrotron Radiation Facility. The current project extends that heritage with NGSolve integration, open-boundary engineering methods, high-order formulations, optimization, native MATLAB/Simulink interfaces, and AI-oriented automation.

We gratefully acknowledge Joachim Schöberl and the Netgen/NGSolve development team and community for the numerical foundation that makes these workflows possible. NGSolve provides the finite-element spaces, geometric mappings, quadrature, assembly, and field evaluation on which Radia builds its electromagnetic applications. Radia also integrates the HACApK H-matrix library, sparseSolv, Netgen, Gmsh, build123d, Coreform Cubit, and the broader Python/MATLAB scientific ecosystems.

The repository contains components under different compatible terms, including the BSD-style Radia core, MIT-licensed HACApK, MPL-2.0 sparseSolv integration, and external runtime dependency notices. See LICENSE for the complete terms.

Owner-authored code is licensed under Apache-2.0 from the next releases. See LICENSE, NOTICE and THIRD_PARTY_NOTICES.md. Third-party code and assets retain their original licenses; previously published artifacts are unchanged.