G. W. Zumbusch.
A sparse grid PDE solver.
In H. P. Langtangen, A. M. Bruaset, and E. Quak, editors,
Advances in Software Tools for Scientific Computing, volume 10 of
Lecture Notes in Computational Science and Engineering, chapter 4, pages
133-177. Springer, Berlin, Germany, 2000.
(Proceedings SciTools '98).
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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|logh|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 methods based sparse grid. 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.