Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences

Authors:
M. Griebel
Affiliations:
Univ. of Bonn, Bonn, Germany
Venue:
Computing
Year:
1998

Citing 0
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Abstract

We present a multilevel approach for the solution of partialdifferential equations. It is based on a multiscale basis which isconstructed from a one-dimensional multiscale basis by the tensorproduct approach. Together with the use of hash tables as datastructure, this allows in a simple way for adaptive refinement and is,due to the tensor product approach, well suited for higher dimensionalproblems. Also, the adaptive treatment of partial differentialequations, the discretization (involving finite differences) and thesolution (here by preconditioned BiCG) can be programmed easily. Wedescribe the basic features of the method, discuss the discretization,the solution and the refinement procedures and report on the results ofdifferent numerical experiments.—Author's Abstract