Distributional BEM

Fabian M.E. Duddeck; Oliver Heaviside

Distributional BEM

Fabian M.E. Duddeck
, Oliver Heaviside

Associate Professorship of Computational Mechanics

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

Abstract

To obtain the Fourier transform of the BIE derived above, all quantities have to be extended from Ω to ℝⁿ (the Fourier transformation is defined on ℝⁿ and not on Ω). Formally, this can be done by defining a cutoff distribution χ which is simply one in the interior of Ω and zero outside. Then all quantities are multiplied by χ and finally transformed into Fourier space (windowed Fourier transform). Mathematically this extension and transformation is justified only in the frame of the theory of distributions.

Original language	English
Title of host publication	Fourier BEM
Subtitle of host publication	Generalization of Boundary Element Methods by Fourier Transform
Editors	Fabian M. E. Duddeck
Pages	25-34
Number of pages	10
State	Published - 2002

Publication series

Name	Lecture Notes in Applied and Computational Mechanics
Volume	5
ISSN (Print)	1613-7736

Cite this

@inbook{135036aff38a4186b319ee12a43e9a06,

title = "Distributional BEM",

abstract = "To obtain the Fourier transform of the BIE derived above, all quantities have to be extended from Ω to ℝn (the Fourier transformation is defined on ℝn and not on Ω). Formally, this can be done by defining a cutoff distribution χ which is simply one in the interior of Ω and zero outside. Then all quantities are multiplied by χ and finally transformed into Fourier space (windowed Fourier transform). Mathematically this extension and transformation is justified only in the frame of the theory of distributions.",

author = "Duddeck, \{Fabian M.E.\} and Oliver Heaviside",

year = "2002",

language = "English",

isbn = "9783642077272",

series = "Lecture Notes in Applied and Computational Mechanics",

pages = "25--34",

editor = "Duddeck, \{Fabian M. E.\}",

booktitle = "Fourier BEM",

}

TY - CHAP

T1 - Distributional BEM

AU - Duddeck, Fabian M.E.

AU - Heaviside, Oliver

PY - 2002

Y1 - 2002

N2 - To obtain the Fourier transform of the BIE derived above, all quantities have to be extended from Ω to ℝn (the Fourier transformation is defined on ℝn and not on Ω). Formally, this can be done by defining a cutoff distribution χ which is simply one in the interior of Ω and zero outside. Then all quantities are multiplied by χ and finally transformed into Fourier space (windowed Fourier transform). Mathematically this extension and transformation is justified only in the frame of the theory of distributions.

AB - To obtain the Fourier transform of the BIE derived above, all quantities have to be extended from Ω to ℝn (the Fourier transformation is defined on ℝn and not on Ω). Formally, this can be done by defining a cutoff distribution χ which is simply one in the interior of Ω and zero outside. Then all quantities are multiplied by χ and finally transformed into Fourier space (windowed Fourier transform). Mathematically this extension and transformation is justified only in the frame of the theory of distributions.

UR - https://www.scopus.com/pages/publications/84880174612

M3 - Chapter

AN - SCOPUS:84880174612

SN - 9783642077272

T3 - Lecture Notes in Applied and Computational Mechanics

SP - 25

EP - 34

BT - Fourier BEM

A2 - Duddeck, Fabian M. E.

ER -

Distributional BEM

Abstract

Publication series

Other files and links

Fingerprint

Cite this