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electromagnetics-sim

FDTD/FEM electromagnetics

Meep, Ansys HFSS

SystemTechniques · 13Primitives · 29 electromagnetics-sim Halo exchangedistributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.›B rep topologygeometry · medium: Boundary representation: solids as shells, faces, loops, edges and vertices with geometry attachedDelaunay triangulationgeometry · medium: Bowyer-Watson and incremental flips; maximizes minimum angles, dual of VoronoiFinite elementsnumerics · medium: Writes the PDE in weak form, approximates it with piecewise polynomials on a mesh and assembles a sparse system; handles any geometry.›Gmresnumerics · medium: GMRES with restarts: Arnoldi, Givens rotations, for nonsymmetric sparse systemsIncomplete factorization preconditi…numerics · medium: Sparse approximate LU or Cholesky factors (ILU, IC) that precondition Krylov solvers: fewer iterations than Jacobi, less memory than a direct solve.›Sparse direct solvernumerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.›Unstructured mesh representationnumerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly orderingFast Fourier transformnumerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.›Gpu memory coalescing bankinghardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUsSIMD programminghardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.›Collective communicationml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.›Multigridnumerics · low: Smooths high-frequency error on the fine grid and solves the smooth remainder on coarser grids; O(n) elliptic solves at any resolution.›Periodic boundary conditionsphysics · low: Minimum image convention and wrapping for simulations in periodic boxesEager rendezvous protocoldistributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large onesRdmanetworking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided opsZero-copy I/Onetworking · low: Move bytes between files, sockets and NICs by passing page references instead of copying through user space: sendfile, splice, MSG_ZEROCOPY, kTLS.›Exact geometric predicatesgeometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmeticHalf edge meshgraphics · low: Half-edge mesh connectivity for editable polygon meshesSpace filling curvesgeometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keysConjugate gradientnumerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.›Gaussian quadraturenumerics · low: Approximate an integral by a weighted sum of n function values at roots of orthogonal polynomials; exact for polynomials up to degree 2n-1.›Sparse matrices (CSR)numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.›+ 6 more techniques+ 13 more primitives

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