Towards generating optimised finite element solvers for GPUs from high-level specifications

Abstract We argue that producing maintainable high-performance implementations of finite element methods for multiple targets requires that they are written using a high-level domain-specific language. We make the case for using one such language, the Unified Form Language (UFL), by discussing how it allows the generation of high-performance code from maintainable sources. We support this case by showing that optimal implementations of a finite element solver written for a Graphics Processing Unit and a multicore CPU require the use of different algorithms and data formats that are embodied by the UFL representation. Finally we describe a prototype compiler that generates low-level code from high-level specifications, and outline how the high-level UFL representation can be lowered to facilitate optimisation using existing techniques prior to code generation.