RapidMesh

Tetrahedral and surface meshes for FEM and FVM in pure Rust.

RapidMesh is a tetrahedral and surface mesh generator for finite element and finite volume solvers, in pure Rust. Primitives, booleans, fillets, STEP files and imported meshes assemble into one model through an exact arrangement, with no float snapping. The resulting B-rep carries the true surfaces (quadrics, tori, extrusions, revolutions, NURBS), and the mesh is measured against those, not against their facets.

Meshing runs bottom-up: corners, edges, faces, then each region on its own. Every level is final before the next one uses it, so neighbours share their triangles by construction. Each region is filled by its constrained Delaunay tetrahedralization, grown from its boundary after every boundary segment has been split until it is strongly Delaunay. Refinement adds the interior points, and a local improver removes the last bad tets.

Multi-material models are what this was built for. A Luneburg lens is seven nested shells, each its own region. Every interface is one face of the B-rep, meshed once and shared by the regions on both sides, so the solver never sees a crack that is not in the geometry.

What a solver gets

The mesh comes with what a solver otherwise rebuilds: edge and face topology with orientation signs, the B-rep entity every node, edge and face lies on, and named sets for materials, ports and boundary conditions. For finite elements it comes in second order too, every mid-edge node on the true surface or curve; on a unit ball that takes the volume error from 2.9 % to 0.01 %. For finite volumes the tets, or the polyhedral cells of their median dual at a third to a quarter of the count, go out as an OpenFOAM polyMesh, with the non-orthogonality and skewness checkMesh would report:

mesh = g.mesh()
mesh.write_foam("case", polyhedral=True)  # OpenFOAM, polyhedral cells
mesh.write_inp("part.inp", order=2)       # CalculiX / Abaqus, tet10
mesh.write_msh("part.msh", order=2)       # gmsh, second order

The corpus

A corpus of 223 geometries, CAD parts from STEP files among them, is meshed on every change, compared with a stored baseline for watertightness, slivers and fidelity to the input, and rendered. Against gmsh on 27 of them, RapidMesh takes half the time and has the better smallest dihedral angle on all 27. Solvers use RapidMesh in-process: one call returns the mesh with the topology, signs and named sets they need, and a new budget is one more call.

History

The first mesher I wrote was a 2D QuadTree in 2023, for a quasi-electrostatic finite volume solver of mine. It was written against one solver, which is how RapidMesh is built too.

RapidMesh started in June 2026 to replace gmsh inside the stack. The first versions refined one restricted Delaunay triangulation of the whole model and recovered the boundary afterwards; conformity stayed approximate. The bottom-up mesher replaced it at the end of September 2026, and with it the 3D path went from behind gmsh to ahead of it. In October 2026 RapidMesh widened from electromagnetics to FEM and FVM in general.