@InCollection{ Zumbusch:2000*1, author = {G. W. Zumbusch}, title = {Parallel Adaptively Refined Sparse Grids}, booktitle = {Multigrid Methods {VI}}, publisher = {Springer}, address = {Berlin, Germany}, year = {2000}, pages = {285--292}, editor = {E. Dick and K. Riemslagh and J. Vierendeels}, volume = {14}, note = {(Proceedings EMG 6)}, series = {Lecture Notes in Computational Science and Engineering}, ps = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/emg99.ps.gz} , pdf = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/emg99.pdf} , annote = {unrefereed (only abstracts),parallel}, abstract = {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.} }