Domain decomposition solvers for nonlinear multiharmonic finite element equations

Handle URI:
http://hdl.handle.net/10754/598010
Title:
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Authors:
Copeland, D. M.; Langer, U.
Abstract:
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Citation:
Copeland DM, Langer U (2010) Domain decomposition solvers for nonlinear multiharmonic finite element equations. Journal of Numerical Mathematics 18. Available: http://dx.doi.org/10.1515/JNUM.2010.008.
Publisher:
Walter de Gruyter GmbH
Journal:
Journal of Numerical Mathematics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2010
DOI:
10.1515/JNUM.2010.008
Type:
Article
ISSN:
1570-2820; 1569-3953
Sponsors:
This publication is partially based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and by the Austrian Science Fund 'Fonds zur Forderung der wissenschaftlichen Forschung (FWF)' under the grant P19255.
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Full metadata record

DC FieldValue Language
dc.contributor.authorCopeland, D. M.en
dc.contributor.authorLanger, U.en
dc.date.accessioned2016-02-25T13:10:54Zen
dc.date.available2016-02-25T13:10:54Zen
dc.date.issued2010-01en
dc.identifier.citationCopeland DM, Langer U (2010) Domain decomposition solvers for nonlinear multiharmonic finite element equations. Journal of Numerical Mathematics 18. Available: http://dx.doi.org/10.1515/JNUM.2010.008.en
dc.identifier.issn1570-2820en
dc.identifier.issn1569-3953en
dc.identifier.doi10.1515/JNUM.2010.008en
dc.identifier.urihttp://hdl.handle.net/10754/598010en
dc.description.abstractIn many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.en
dc.description.sponsorshipThis publication is partially based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and by the Austrian Science Fund 'Fonds zur Forderung der wissenschaftlichen Forschung (FWF)' under the grant P19255.en
dc.publisherWalter de Gruyter GmbHen
dc.subjectDomain decompositionen
dc.subjectFinite element methoden
dc.subjectNonlinear parabolic problemsen
dc.subjectTime-harmonic excitationen
dc.titleDomain decomposition solvers for nonlinear multiharmonic finite element equationsen
dc.typeArticleen
dc.identifier.journalJournal of Numerical Mathematicsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionJohannes Kepler Universitat Linz, Linz, Austriaen
kaust.grant.numberKUS-C1-016-04en
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