Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

Dylan Copeland; Michael Kolmbauer; Ulrich Langer

doi:10.1007/978-3-642-11304-8_34

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

Dylan Copeland, Michael Kolmbauer, Ulrich Langer

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10 Scopus citations

Abstract

The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

Original language	English (US)
Title of host publication	Domain Decomposition Methods in Science and Engineering XIX
Publisher	Springer Nature
Pages	301-308
Number of pages	8
ISBN (Print)	9783642113031
DOIs	https://doi.org/10.1007/978-3-642-11304-8_34
State	Published - Oct 5 2010
Externally published	Yes

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title = "Domain Decomposition Solvers for Frequency-Domain Finite Element Equations",

abstract = "The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. {\textcopyright} 2011 Springer-Verlag Berlin Heidelberg.",

author = "Dylan Copeland and Michael Kolmbauer and Ulrich Langer",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The authors gratefully acknowledge the financial support by the Austrian ScienceFund (FWF) under the grant P19255 and by the Award No. KUS-C1-016-04, madeby King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/978-3-642-11304-8_34",

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AU - Copeland, Dylan

AU - Kolmbauer, Michael

AU - Langer, Ulrich

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The authors gratefully acknowledge the financial support by the Austrian ScienceFund (FWF) under the grant P19255 and by the Award No. KUS-C1-016-04, madeby King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/10/5

Y1 - 2010/10/5

N2 - The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

AB - The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

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BT - Domain Decomposition Methods in Science and Engineering XIX

PB - Springer Nature

ER -

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

Abstract

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