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A fast sparse grid based space-time boundary element method for the nonstationary heat equation

Harbrecht, Helmut and Tausch, Johannes. (2018) A fast sparse grid based space-time boundary element method for the nonstationary heat equation. Numerische Mathematik, 140 (1). pp. 239-264.

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Official URL: https://edoc.unibas.ch/65034/

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0029-599X
e-ISSN:0945-3245
Note:Publication type according to Uni Basel Research Database: Journal article -- The final publication is available at Springer, see DOI link
Language:English
Identification Number:
Last Modified:12 Sep 2018 09:21
Deposited On:12 Sep 2018 09:21

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