Discontinuous Galerkin method on three-dimensional tetrahedral grids. The use of template metaprogramming of the C++ language

Abstract

Many mathematical physics problems have great computational complexity, especially when they are solved on large-scale three-dimensional grids. The discontinuous Galerkin method is just an example of this kind. Therefore, reduction of the amount of computation is very a topical task. One of the possible ways to reduce the amount of computation is to move some of the computations to the compilation stage. With the appearance of templates, C++ provides such an opportunity. The paper demonstrates the use of template metaprogramming to speed up computations in the discontinuous Galerkin method. In addition, template metaprogramming sometimes simplifies the algorithm at the expense of its generalization.