TSFC: A Structure-Preserving Form Compiler

Homolya, Miklós; Mitchell, Lawrence; Luporini, Fabio; Ham, David A.

Abstract

A form compiler takes a high-level description of the weak form of partial differential equations and produces low-level code that carries out the finite element assembly. In this paper we present the Two-Stage Form Compiler (TSFC), a new form compiler with the main motivation being to maintain the structure of the input expression as long as possible. This facilitates the application of optimizations at the highest possible level of abstraction. TSFC features a novel, structure-preserving method for separating the contributions of a form to the subblocks of the local tensor in discontinuous Galerkin problems. This enables us to preserve the tensor structure of expressions longer through the compilation process than is possible with other form compilers. This is also achieved in part by a two-stage approach that cleanly separates the lowering of finite element constructs to tensor algebra in the first stage, from the scheduling of those tensor operations in the second stage. TSFC also efficiently traverses complicated expressions, and experimental evaluation demonstrates good compile-time performance even for highly complex forms.

Citation

Homolya, M., Mitchell, L., Luporini, F., & Ham, D. A. (2018). TSFC: A Structure-Preserving Form Compiler. SIAM Journal on Scientific Computing, 40(3), C401-C428. https://doi.org/10.1137/17m1130642

• Journal Article Type: Article
• Acceptance Date: Apr 6, 2018
• Online Publication Date: Jun 26, 2018
• Publication Date: Jun 26, 2018
• Deposit Date: Aug 1, 2018
• Publicly Available Date: Aug 2, 2018
• Journal: SIAM Journal on Scientific Computing
• Print ISSN: 1064-8275
• Electronic ISSN: 1095-7197
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 3
• Pages: C401-C428
• DOI: https://doi.org/10.1137/17m1130642
• Public URL: https://durham-repository.worktribe.com/output/1324887
• Related Public URLs: https://arxiv.org/pdf/1705.03667.pdf