TSFC: a structure-preserving form compiler

TL;DR

TSFC is a novel form compiler that preserves the structure of input expressions to enable high-level optimizations and efficiently handles complex finite element forms, especially in discontinuous Galerkin methods.

Contribution

Introduces a two-stage, structure-preserving form compiler that maintains tensor structure longer and separates lowering from scheduling for improved optimization.

Findings

Good compile-time performance on complex forms

Effective preservation of tensor structure in discontinuous Galerkin problems

Enhanced optimization potential at high abstraction levels

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 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 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.