GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

Abstract

Abstract In this paper, we present a matrix assembly technique for arbitrary polynomial order finite element simulations on simplex meshes for graphics processing units (GPU). Compared to the current state of the art in GPU‐based matrix assembly, we avoid the need for an intermediate sparse matrix and perform assembly directly into the final, GPU‐optimized data structure. Thereby, we avoid the resulting 180 % to 600 % memory overhead, depending on polynomial order, and associated allocation time, while simplifying the assembly code and using a more compact mesh representation. We compare our method with existing algorithms and demonstrate significant speedups.