nanofem

A 3D finite element electromagnetic field solver in one Rust file, capped at 1000 lines of code.

nanofem solves the time harmonic curl-curl equation for the electric field with first order Nedelec edge elements on tetrahedra and reports scattering parameters at lumped ports, in one Rust source file capped at 1000 lines of code. The mesh comes from Gmsh and the setup is a text deck that maps physical group names to materials, boundaries and ports. Perfect electric conductors, a first order absorbing boundary, perfectly matched layers, magnetic symmetry planes, dielectric loss, volume conductivity and conductor sheets with the skin effect all fit.

Three decisions buy the room

Sorting the mesh vertices on input makes every local edge run from the lower to the higher global node. Neighboring elements then agree on their Whitney functions by construction, which is what keeps orientation signs out of the assembly, the ports and the field export alike.

Every matrix entry carries four coefficients against the basis 1, k0, k0 squared and the square root of k0. A loss tangent, a volume conductivity and a conductor sheet with its square root surface resistance all land on one of those four, so a sweep assembles once no matter how many loss mechanisms are in the model.

Storing the PML stretch separately from the permittivity lets the conduction current reuse the mass entry instead of building a second one.

The system is complex symmetric and solved directly: geometric nested dissection, then a sparse LDLT, equilibrated with the inverse square root of the diagonal, which cuts the pivot spread by more than a factor of six at low frequency. One step of iterative refinement per solve against the unscaled matrix follows, so the reported residual is measured.

History

I already had RapidFEM for the production work, which is a much larger body of code. The hard part of FEM is the meshing, and Gmsh is state of the art there. The formulation itself is not complicated, so 1000 lines looked like enough to find out, with the mesh coming in from outside as the natural cut.

The linear solver usually comes from outside as well, PARDISO or Accelerate or my own RSLAB . Here it fit in the budget, and I wanted no dependencies at all, so the ordering and the factorization sit in the file with everything else. It ended at 954.

The report is sized to match, short enough to read next to the code in a day.

nanospice asks the same question of circuit simulation.