COFFEE: an Optimizing Compiler for Finite Element Local Assembly

TL;DR

COFFEE is a domain-specific compiler designed to optimize local assembly kernels in finite element methods, significantly enhancing performance through vectorization and register optimization.

Contribution

It introduces a systematic, domain-aware compilation approach for finite element local assembly kernels, improving execution efficiency over traditional methods.

Findings

Achieves significant performance improvements in finite element local assembly.

Effectively enhances SIMD vectorization and register locality.

Demonstrates benefits across various finite-element forms.

Abstract

The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a problem-specific kernel to numerically evaluate an integral for each element in the discretized problem domain. Since the domain size can be huge, executing efficient kernels is fundamental. Their op- timization is, however, a challenging issue. Even though affine loop nests are generally present, the short trip counts and the complexity of mathematical expressions make it hard to determine a single or unique sequence of successful transformations. Therefore, we present the design and systematic evaluation of COF- FEE, a domain-specific compiler for local assembly kernels. COFFEE manipulates abstract syntax trees generated from a high-level domain-specific language for PDEs by introducing domain-aware composable optimizations aimed at improving instruction-level parallelism, especially SIMD vectorization, and register locality. It then generates C code including vector intrinsics. Experiments using a range of finite-element forms of increasing complexity show that significant performance improvement is achieved.