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

Harbrecht, Helmut and Tausch, Johannes. (2016) A fast sparse grid based space-time boundary element method for the nonstationary heat equation. Preprints Fachbereich Mathematik, 2016 (32).

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Official URL: https://edoc.unibas.ch/69949/

## 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 $\mathcal{H}$-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)12 Special Collections > Preprints Fachbereich Mathematik Harbrecht, Helmut Preprint Universität Basel English 10.5451/unibas-ep69949 22 Apr 2019 22:07 28 Mar 2019 09:51

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