G. W. Zumbusch.
Parallel adaptively refined sparse grids.
In E. Dick, K. Riemslagh, and J. Vierendeels, editors, Multigrid
Methods VI, volume 14 of Lecture Notes in Computational Science and
Engineering, pages 285-292. Springer, Berlin, Germany, 2000.
(Proceedings EMG 6).
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A parallel version of a finite difference discretization of PDEs on sparse grids is proposed. Sparse grids or hyperbolic crosspoints can be used for the efficient representation of solutions of a boundary value problem, especially in high dimensions, because the number of grid points depends only weakly on the dimension. So far only the `combination' technique for regular sparse grids was available on parallel computers. However, the new approach allows for arbitrary, adaptively refined sparse grids. The efficient parallelisation is based on a dynamic load-balancing approach with space-filling curves.