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<table>
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<tr>
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<th colspan="2">Optimized Schwarz domain decomposition methods for time-harmonic wave problems</th>
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</tr>
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<tr>
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<td style="text-align:center"><img src="GetDDM_screenshot1.png" width=100%></td>
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<td style="text-align:center"><img src="GetDDM_screenshot2.png" width=100%></td>
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</tr>
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<tr>
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<th colspan="2">Browse <a href="https://gitlab.onelab.info/doc/models/tree/master/GetDDM">model files</a>
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— Download <a href="http://onelab.info/files/GetDDM.zip">zip archive</a></th>
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</tr>
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</table>
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## Quick start
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To run the models, open `main.pro` with Gmsh.
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(For parallel computations you will have to [recompile GetDP with MPI
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support](https://gitlab.onelab.info/getdp/getdp/wikis/GetDP-compilation). Sample
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[SLURM](https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_slurm.sh)
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and [PBS
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scripts](https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_pbs.sh)
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are provided to to run on HPC clusters.)
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## Additional information
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The formulations implement non-overlapping Schwarz domain decomposition methods
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for time-harmonic acoustic and electromagnetic wave problems. Several families
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of transmission conditions are implemented: zeroth- and second-order optimized
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conditions [1-6], Padé-localized square-root conditions [7-8] and PML conditions
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[9]. Several variants of the double-sweep preconditioner [9] are also
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implemented.
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For more information about these methods as well as the implementation, please
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refer to [GetDDM: an Open Framework for Testing Optimized Schwarz Methods for
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Time-Harmonic Wave
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Problems](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf)
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[10].
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## References
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1. B. Després, Méthodes de Décomposition de Domaine pour les Problèmes de
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Propagation d'Ondes en Régime Harmonique. Le Théorème de Borg pour l'Equation de
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Hill Vectorielle, PhD Thesis, Paris VI University, France, 1991.
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2. B. Després, P. Joly and J. Roberts, A domain decomposition method for the
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harmonic Maxwell equations, Iterative methods in linear algebra (Brussels,
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1991), pp. 475-484, North-Holland, 1992.
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3. M. Gander, F. Magoulès and F. Nataf, Optimized Schwarz methods without
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overlap for the Helmholtz equation}, SIAM Journal on Scientific Computing,
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24(1), pp. 38-60, 2002.
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4. V. Dolean, M. Gander and L. Gerardo-Giorda, Optimized Schwarz methods for
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Maxwell's equations, SIAM Journal on Scientific Computing, 31(3), pp. 2193-2213,
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2009.
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5. A. Bendali and Y. Boubendir, Non-Overlapping Domain Decomposition Method for
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a Nodal Finite Element Method, Numerische Mathematik 103(4), pp.515-537, (2006).
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6. V. Rawat and J.-F. Lee, Nonoverlapping Domain Decomposition with Second Order
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Transmission Condition for the Time-Harmonic Maxwell's Equations, SIAM Journal
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on Scientific Computing, 32(6), pp. 3584-3603, 2010.
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7. Y. Boubendir, X. Antoine and C. Geuzaine. [A quasi-optimal non-overlapping
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domain decomposition algorithm for the Helmholtz
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equation](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_helmholtz_preprint.pdf).
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Journal of Computational Physics 231 (2), 262-280, 2012.
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8. M. El Bouajaji, X. Antoine and C. Geuzaine. [Approximate local
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magnetic-to-electric surface operators for time-harmonic Maxwell’s
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equations](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/osrc_maxwell_preprint.pdf).
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Journal of Computational Physics 279 241-260, 2014.
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9. A. Vion and C. Geuzaine. [Double sweep preconditioner for optimized Schwarz
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methods applied to the Helmholtz
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problem](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_double_sweep_preprint.pdf).
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Journal of Computational Physics 266, 171-190, 2014.
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10. B. Thierry, A.Vion, S. Tournier, M. El Bouajaji, D. Colignon, N. Marsic,
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X. Antoine, C. Geuzaine. [GetDDM: an Open Framework for Testing Optimized
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Schwarz Methods for Time-Harmonic Wave
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Problems](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf).
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Computer Physics Communications 203, 309-330, 2016.
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----
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*Models developed by X. Antoine, Y. Boubendir, M. El Bouajaji, D. Colignon,
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@geuzaine, @marsic, @thierry, S. Tournier and A. Vion. This work was
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funded in part by the Belgian Science Policy (IAP P6/21 and P7/02), the Belgian
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French Community (ARC 09/14-02), the Walloon Region (WIST3 No 1017086 ONELAB and
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ALIZEES), the Agence Nationale pour la Recherche (ANR-09-BLAN-0057-01 MicroWave)
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and the EADS Foundation (grant 089-1009-1006 High-BRID).* |
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\ No newline at end of file |