Difference between revisions of "Domain decomposition methods for waves"
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To run the models, open '''main.pro''' with Gmsh. (This is for demonstration uses only. For actual, parallel computations, you should compile GetDP and Gmsh with MPI support: see [[GetDDM]]). | To run the models, open '''main.pro''' with Gmsh. (This is for demonstration uses only. For actual, parallel computations, you should compile GetDP and Gmsh with MPI support: see [[GetDDM]]). | ||
| − | The formulations implement non-overlapping Schwarz domain decomposition methods for the Helmholtz equation and for the time-harmonic Maxwell system. Several families of transmission conditions are implemented: zeroth- and second-order optimized conditions<ref name=Despres1 /><ref name=Despres2 /><ref name=Gander1 /><ref name=Gander2 /><ref name=Boubendir1 /><ref name=RawatL10 />, new Padé-localized square-root conditions<ref name=BoubAntGeuz2012 /><ref name=ElBouAntGeuz2014 /> and PML conditions. | + | The formulations implement non-overlapping Schwarz domain decomposition methods for the Helmholtz equation and for the time-harmonic Maxwell system. Several families of transmission conditions are implemented: zeroth- and second-order optimized conditions<ref name=Despres1 /><ref name=Despres2 /><ref name=Gander1 /><ref name=Gander2 /><ref name=Boubendir1 /><ref name=RawatL10 />, new Padé-localized square-root conditions<ref name=BoubAntGeuz2012 /><ref name=ElBouAntGeuz2014 /> and PML conditions. Several variants of the recently proposed double-sweep preconditioner<ref name=VionGeuz2014> are also implemented. |
| − | + | <!-- For more information about these methods, please refer to the following paper, which summarizes the mathematics and provides detailed explanations about the implementation. | |
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| + | If you use the codes provided on this page, please cite the following reference in your work: | ||
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== References == | == References == | ||
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<ref name=RawatL10>V. Rawat and J.-F. Lee, Nonoverlapping Domain Decomposition with Second Order Transmission Condition for the Time-Harmonic Maxwell's Equations, SIAM Journal on Scientific Computing, 32(6), pp. 3584-3603, 2010.</ref> | <ref name=RawatL10>V. Rawat and J.-F. Lee, Nonoverlapping Domain Decomposition with Second Order Transmission Condition for the Time-Harmonic Maxwell's Equations, SIAM Journal on Scientific Computing, 32(6), pp. 3584-3603, 2010.</ref> | ||
| − | <ref name=BoubAntGeuz2012>Y. Boubendir, X. Antoine | + | <ref name=BoubAntGeuz2012>Y. Boubendir, X. Antoine and C. Geuzaine. [http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_helmholtz_preprint.pdf A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation]. Journal of Computational Physics 231 (2), 262-280, 2012.</ref> |
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| + | <ref name=ElBouAntGeuz2014>M. El Bouajaji, X. Antoine and C. Geuzaine. Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell’s equations, Journal of Computational Physics, accepted for publication, 2014.</ref> | ||
| − | <ref name= | + | <ref name=VionGeuz2014>A. Vion and C. Geuzaine. Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem. Journal of Computational Physics 266, 171-190, 2014.</ref> |
</references> | </references> | ||
Revision as of 07:02, 2 June 2015
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Optimized Schwarz domain decomposition methods for time-harmonic wave problems
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Download model archive (ddm_waves.zip) |
Introduction
To run the models, open main.pro with Gmsh. (This is for demonstration uses only. For actual, parallel computations, you should compile GetDP and Gmsh with MPI support: see GetDDM).
The formulations implement non-overlapping Schwarz domain decomposition methods for the Helmholtz equation and for the time-harmonic Maxwell system. Several families of transmission conditions are implemented: zeroth- and second-order optimized conditions[1][2][3][4][5][6], new Padé-localized square-root conditions[7][8] and PML conditions. Several variants of the recently proposed double-sweep preconditionerCite error: Closing </ref> missing for <ref> tag
</references>
Models developed by X. Antoine, Y. Boubendir, M. El Bouajaji, D. Colignon, C. Geuzaine, N. Marsic, B. Thierry, S. Tournier and A. Vion. This work was funded in part by the Belgian Science Policy (IAP P6/21 and P7/02), the Belgian French Community (ARC 09/14-02), the Walloon Region (WIST3 No 1017086 ONELAB and ALIZEES), the Agence Nationale pour la Recherche (ANR-09-BLAN-0057-01 MicroWave) and the EADS Foundation (grant 089-1009-1006 High-BRID).
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