A Time-Adaptive Space-Time FMM for the Heat Equation

Raphael Watschinger; Günther Of

doi:10.1515/cmam-2022-0117

A Time-Adaptive Space-Time FMM for the Heat Equation

Raphael Watschinger, Günther Of^*

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-review

Abstract

We present a new time-adaptive FMM for a space-time boundary element method for the heat equation. The method extends the existing parabolic FMM by adding new operations that allow for an efficient treatment of tensor product meshes which are adaptive in time. We analyze the efficiency of the new operations and the approximation quality of the related kernel expansions and present numerical experiments that reveal the benefits of the new method.

Original language	English
Pages (from-to)	445-471
Number of pages	27
Journal	Computational Methods in Applied Mathematics
Volume	23
Issue number	2
Early online date	6 Dec 2022
DOIs	https://doi.org/10.1515/cmam-2022-0117
Publication status	Published - 1 Apr 2023

Keywords

Adaptivity
Boundary Element Method
FMM
Heat Equation
Space-Time Method

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1515/cmam-2022-0117

Cite this

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title = "A Time-Adaptive Space-Time FMM for the Heat Equation",

abstract = "We present a new time-adaptive FMM for a space-time boundary element method for the heat equation. The method extends the existing parabolic FMM by adding new operations that allow for an efficient treatment of tensor product meshes which are adaptive in time. We analyze the efficiency of the new operations and the approximation quality of the related kernel expansions and present numerical experiments that reveal the benefits of the new method.",

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N2 - We present a new time-adaptive FMM for a space-time boundary element method for the heat equation. The method extends the existing parabolic FMM by adding new operations that allow for an efficient treatment of tensor product meshes which are adaptive in time. We analyze the efficiency of the new operations and the approximation quality of the related kernel expansions and present numerical experiments that reveal the benefits of the new method.

AB - We present a new time-adaptive FMM for a space-time boundary element method for the heat equation. The method extends the existing parabolic FMM by adding new operations that allow for an efficient treatment of tensor product meshes which are adaptive in time. We analyze the efficiency of the new operations and the approximation quality of the related kernel expansions and present numerical experiments that reveal the benefits of the new method.

KW - Adaptivity

KW - Boundary Element Method

KW - FMM

KW - Heat Equation

KW - Space-Time Method

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A Time-Adaptive Space-Time FMM for the Heat Equation

Abstract

Keywords

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FWF - Besthea - Space-time boundary element methods for the heat equation

Cite this

A Time-Adaptive Space-Time FMM for the Heat Equation

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Other files and links

Fingerprint

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FWF - Besthea - Space-time boundary element methods for the heat equation

Cite this