GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

• Published in: Computer graphics forum Vol. 37; no. 7; pp. 443 - 454
• Main Authors: Mueller‐Roemer, J. S., Stork, A.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01-10-2018
• Subjects: Assembly; CCS Concepts; Computer simulation; Computing methodologies → Massively parallel and high‐performance simulations; Data structures; Finite element method; Graphics processing units; Graphics processors; Massively parallel algorithms; Mathematical analysis; Mathematics of computing → Combinatoric problems; Physical simulation; Polynomials; State of the art
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13581

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.