RapidMesh

2D and 3D mesh generation for electromagnetic FEM and MoM in pure Rust.

RapidMesh is a tetrahedral mesh generator for 3D electromagnetic FEM with a first-class 2D path for 2.5D MoM solvers, in pure Rust. Solid primitives (box, cylinder, sphere, cone, torus, prism, sweep, loft) assemble into a tagged complex; exact-arithmetic CSG booleans (exact predicates, no float snapping) produce a non-manifold B-rep with exactly conforming material interfaces.

Meshing is dimensionally hierarchical: corners, then edges, then faces, then the volume, freezing each level before the next consumes it. Within every dimension, error-driven adaptive sampling combines with variational point relaxation for quality: sizing-weighted Lloyd relaxation on edges and faces, optimal-Delaunay relaxation in the volume, plus sliver exudation and edge removal targeting the minimal dihedral angle. The frozen surface triangulation is a hard constraint on the volume Delaunay, which is what makes the boundary watertight by construction. The sizing and chart formulae for every curve and surface modality are derived with a computer-algebra system, not approximated ad hoc.

Meshing is budgeted: mesh(target_elements=N) retunes the global size scale over a few remeshes, since the element count scales with the third power of the scale, and lands within a few percent of N while the relative refinement from curvature and sizing keeps its shape. Surface budgets act as a cap instead: the count-driven refinement resolves the sizing field but stops at the triangle budget, split across patches by area, spending its last splits on the worst-quality triangles. Solvers can plan a mesh the way RSLAB plans a factorization: the cost is decided before the run, not discovered after.

The 2D path

The same core that meshes each 3D surface patch is the standalone planar mesher for MoM: graded, sliver-free constrained Delaunay triangulation of tagged polygons with holes, with RWG edge topology derived in the same bundle. A target_count budget scales the sizing field so the mesh lands near the requested triangle count, shared across all metal layers:

import rapidmesh as rm

layers = rm.mesh_layers(groups, sizing, target_count=20_000)
# points, tris, tags, RWG edges and boundary topology per layer

Overlapping regions within a group weld into one electrically continuous component; separate metal layers never merge.

Validated, not assumed

A validation corpus of 101 geometries (primitives, booleans, multi-region assemblies, RF passives, STL/OBJ imports) is re-run and re-rendered on every full run. The API serves the solver as an oracle: mesh representations carry exactly what FEM assembly and refinement need. It is built to replace gmsh inside the stack: one less external dependency, one more deterministic component.

History

RapidMesh started in June 2026 with one goal: replace gmsh inside the stack with a deterministic, embeddable mesher. The 2D path is now the mesher inside RapidMoM ; the 3D path is built to take over RapidFEM 's meshing, which still runs on gmsh today.