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|
|Number of pages||8|
|State||Published - Oct 5 2010|
Bibliographical noteKAUST 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.