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Published in:
Robust Block Preconditioners for Biot’s Model Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Preconditioned Space-Time Boundary Element Methods for the One-Dimensional Heat Equation

Authors : Stefan Dohr, Olaf Steinbach

Published in: Domain Decomposition Methods in Science and Engineering XXIV

Publisher: Springer International Publishing

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Abstract

In this note we describe a space-time boundary element discretization of the heat equation and an efficient and robust preconditioning strategy which is based on the use of boundary integral operators of opposite orders, but which requires a suitable stability condition for the boundary element spaces used for the discretization. We demonstrate the method for the simple spatially one-dimensional case. However, the presented results, particularly the stability analysis of the boundary element spaces, can be used to extend the method to the two- and three-dimensional problem.

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previous chapter Is Minimising the Convergence Rate a Good Choice for Efficient Optimized Schwarz Preconditioning in Heterogeneous Coupling? The Stokes-Darcy Case
next chapter On High-Order Approximation and Stability with Conservative Properties
Literature
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O. Steinbach, W.L. Wendland, Efficient preconditioners for boundary element methods and their use in domain decomposition, in Domain Decomposition Methods in Sciences in Engineering: 8th International Conference, Beijing, China, ed. by R. Glowinski et al. (Wiley, Hoboken, 1997), pp. 3–18
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Metadata
Title
Preconditioned Space-Time Boundary Element Methods for the One-Dimensional Heat Equation
Authors
Stefan Dohr
Olaf Steinbach
Copyright Year
2018
Book
Domain Decomposition Methods in Science and Engineering XXIV

Print ISBN: 978-3-319-93872-1

Electronic ISBN: 978-3-319-93873-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-93873-8_22

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