A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization

Abstract

Sparse grids are an efficient approximation method for functions, especially in higher dimensions d≥3. Compared to regular, uniform grids of a mesh parameter h, which contain h −d points in d dimensions, sparse grids require only h −1| log h|d−1 points due to a truncated, tensor-product multi-scale basis representation. The purpose of this paper is to survey some activities for the solution of partial differential equations with method based sparse grids. Furthermore some aspects of sparse grids are discussed such as adaptive grid refinement, parallel computing, a space-time discretization scheme and the structure of a code to implement these methods.KeywordsRegular GridHash TableGrid RefinementSparse GridHilbert CurveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.