Finite element assembly using an embedded domain specific language

Abstract

In finite element methods, numerical simulation of the problem requires the generation of a linear system based on an integral form of a problem. Using C++ meta-programming techniques, a method is developed that allows writing code that stays close to the mathematical formulation. We explain the specifics of our method, which relies on the Boost. Proto framework to simplify the evaluation of our language. Some practical examples are elaborated, together with an analysis of the performance. The abstraction overhead is quantified using benchmarks.