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A fast sparse grid based space-time boundary element method for the nonstationary heat equation
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 4482419
Author(s) Harbrecht, Helmut; Tausch, Johannes
Author(s) at UniBasel Harbrecht, Helmut
Year 2018
Title A fast sparse grid based space-time boundary element method for the nonstationary heat equation
Journal Numerische Mathematik
Volume 140
Number 1
Pages / Article-Number 239-264
Keywords boundary element methods, heat equation, sparse grids
Abstract This article presents a fast sparse grid based space-time boundary element method for the solution of the nonstationary heat equation. We make an indirect ansatz based on the thermal single layer potential which yields a first kind integral equation. This integral equation is discretized by Galerkin's method with respect to the sparse tensor product of the spatial and temporal ansatz spaces. By employing the H -matrix and Toeplitz structure of the resulting discretized operators, we arrive at an algorithm which computes the approximate solution in a complexity that essentially corresponds to that of the spatial discretization. Nevertheless, the convergence rate is nearly the same as in case of a traditional discretization in full tensor product spaces.
Publisher Springer
ISSN/ISBN 0029-599X ; 0945-3245
edoc-URL https://edoc.unibas.ch/65034/
Full Text on edoc Restricted
Digital Object Identifier DOI 10.1007/s00211-018-0963-5
ISI-Number WOS:000440098200007
Document type (ISI) Article
 
   


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