Automatically assigned DDC number: 515353

Manually assigned DDC number: 515353

Number of references: 8

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

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

Description: We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which is constructed from a onedimensional multiscale basis by the tensor product approach. Together with the use of hash tables as data structure, this allows in a simple way for adaptive refinement and is, due to the tensor product approach, well suited for higher dimensional problems. Also, the adaptive treatment of partial differential equations, the discretization (involving finite differences) and the solution (here by preconditioned BiCG) can be programmed easily. We describe the basic features of the method, discuss the discretization, the solution and the refinement procedures and report on the results of different numerical experiments. AMS subject classifications: 65N06, 65N50, 68Y99, 68P05. Key words: Sparse grids, finite difference, multiscale method, hash tables. 1 Introduction In this paper, we present an adaptive multilevel approach for the solution ...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1998-06-02

Pubyear: 1998

Format: ps

Identifier: http://citeseer.ist.psu.edu/190150.html

Source: http://wwwwissrech.iam.uni-bonn.de/research/pub/varna.ps.gz

Language: en

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