Domain decomposition solvers for nonlinear multiharmonic finite element equations

D. M. Copeland, U. Langer

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)157-175
Number of pages19
JournalJournal of Numerical Mathematics
Volume18
Issue number3
DOIs
StatePublished - Jan 2010
Externally publishedYes

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