Automated code generation for discontinuous Galerkin methods

TL;DR

This paper introduces a compiler-based method that translates high-level mathematical descriptions of discontinuous Galerkin finite element methods into efficient low-level code, enabling rapid and flexible simulation of various PDEs.

Contribution

It presents a novel compiler approach that automates code generation from mathematical notation for discontinuous Galerkin methods, improving efficiency and flexibility.

Findings

Successfully generated code for Poisson, biharmonic, advection--diffusion, and Stokes equations.

Demonstrated the approach's ability to handle different spatial dimensions.

Achieved efficient code suitable for complex PDEs.

Abstract

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates efficient code in a standard programming language. This facilitates the rapid generation of efficient code for general equations in varying spatial dimensions. Key concepts underlying the compiler approach and the automated generation of computer code are elaborated. The approach is demonstrated for a range of common problems, including the Poisson, biharmonic, advection--diffusion and Stokes equations.