Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {G. W. Zumbusch},
  title = {A Sparse Grid {PDE} Solver},
  booktitle = {Advances in Software Tools for Scientific Computing},
  pages = {133--177},
  publisher = {Springer},
  address = {Berlin, Germany},
  year = {2000},
  editor = {H. P. Langtangen and A. M. Bruaset and E. Quak},
  volume = {10},
  series = {Lecture Notes in Computational Science and Engineering},
  chapter = {4},
  note = {(Proceedings SciTools '98)},
  ps = { 1},
  pdf = { 1},
  annote = {refereed,parallel},
  zmath = {},
  abstract = {Sparse grids are an efficient approximation method for
		  functions, especially in higher dimensions $d \ge 3$.
		  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 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.}