The Fourier boundary element method and its singularities

Fabian Duddeck

The Fourier boundary element method and its singularities

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Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

One of the limitations of boundary element methods (BEM) lies in their need for a fundamental solution. In many engineering problems, this function is not known analytically but constructed numerically. The corresponding precomputed values are stored in tables and later - during the computation - the required values are interpolated. To overcome this drawback and to accelerate the computation of the BEM, a Fourier transformed boundary element method was proposed. The focus of this paper is the treatment of singular and hypersingular integrals of this Fourier BEM. It can be shown easily that all strong and hypersingular values cancel. The computation of the singular integrals is hence straightforward in the Fourier space and can be used in traditional BEM approaches.

Original language	English
Title of host publication	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Pages	1100-1104
Number of pages	5
State	Published - 2005
Externally published	Yes
Event	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics - Boston, MA, United States Duration: 14 Jun 2005 → 17 Jun 2005

Publication series

Name	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Conference

Conference	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Country/Territory	United States
City	Boston, MA
Period	14/06/05 → 17/06/05

Keywords

Boundary element method
Distribution theory
Engineering problems
Singular and hypersingular integrals

Cite this

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title = "The Fourier boundary element method and its singularities",

abstract = "One of the limitations of boundary element methods (BEM) lies in their need for a fundamental solution. In many engineering problems, this function is not known analytically but constructed numerically. The corresponding precomputed values are stored in tables and later - during the computation - the required values are interpolated. To overcome this drawback and to accelerate the computation of the BEM, a Fourier transformed boundary element method was proposed. The focus of this paper is the treatment of singular and hypersingular integrals of this Fourier BEM. It can be shown easily that all strong and hypersingular values cancel. The computation of the singular integrals is hence straightforward in the Fourier space and can be used in traditional BEM approaches.",

keywords = "Boundary element method, Distribution theory, Engineering problems, Singular and hypersingular integrals",

author = "Fabian Duddeck",

year = "2005",

language = "English",

isbn = "0080444814",

series = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics",

pages = "1100--1104",

booktitle = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics",

note = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics ; Conference date: 14-06-2005 Through 17-06-2005",

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T1 - The Fourier boundary element method and its singularities

AU - Duddeck, Fabian

PY - 2005

Y1 - 2005

N2 - One of the limitations of boundary element methods (BEM) lies in their need for a fundamental solution. In many engineering problems, this function is not known analytically but constructed numerically. The corresponding precomputed values are stored in tables and later - during the computation - the required values are interpolated. To overcome this drawback and to accelerate the computation of the BEM, a Fourier transformed boundary element method was proposed. The focus of this paper is the treatment of singular and hypersingular integrals of this Fourier BEM. It can be shown easily that all strong and hypersingular values cancel. The computation of the singular integrals is hence straightforward in the Fourier space and can be used in traditional BEM approaches.

AB - One of the limitations of boundary element methods (BEM) lies in their need for a fundamental solution. In many engineering problems, this function is not known analytically but constructed numerically. The corresponding precomputed values are stored in tables and later - during the computation - the required values are interpolated. To overcome this drawback and to accelerate the computation of the BEM, a Fourier transformed boundary element method was proposed. The focus of this paper is the treatment of singular and hypersingular integrals of this Fourier BEM. It can be shown easily that all strong and hypersingular values cancel. The computation of the singular integrals is hence straightforward in the Fourier space and can be used in traditional BEM approaches.

KW - Boundary element method

KW - Distribution theory

KW - Engineering problems

KW - Singular and hypersingular integrals

UR - http://www.scopus.com/inward/record.url?scp=80053447242&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053447242

SN - 0080444814

SN - 9780080444819

T3 - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

SP - 1100

EP - 1104

BT - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

T2 - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Y2 - 14 June 2005 through 17 June 2005

ER -

The Fourier boundary element method and its singularities

Abstract

Publication series

Conference

Keywords

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