Automated code generation for discontinuous Galerkin methods. (English) Zbl 1189.65283
Summary: 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.
MSC:
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
68N20 | Theory of compilers and interpreters |
65Y15 | Packaged methods for numerical algorithms |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35J25 | Boundary value problems for second-order elliptic equations |
35J40 | Boundary value problems for higher-order elliptic equations |