Domain-decomposition-methods-for-waves.md

+<table>
+  <tr>
+    <th colspan="2">Optimized Schwarz domain decomposition methods for time-harmonic wave problems</th>
+  </tr>
+  <tr>
+    <td style="text-align:center"><img src="GetDDM_screenshot1.png" width=100%></td>
+    <td style="text-align:center"><img src="GetDDM_screenshot2.png" width=100%></td>
+  </tr>
+  <tr>
+    <th colspan="2">Browse <a href="https://gitlab.onelab.info/doc/models/tree/master/GetDDM">model files</a>
+    &mdash; Download <a href="http://onelab.info/files/GetDDM.zip">zip archive</a></th>
+  </tr>
+</table>
+
+## Quick start
+
+To run the models, open `main.pro` with Gmsh.
+
+(For parallel computations you will have to [recompile GetDP with MPI
+ support](https://gitlab.onelab.info/getdp/getdp/wikis/GetDP-compilation). Sample
+ [SLURM](https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_slurm.sh)
+ and [PBS
+ scripts](https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_pbs.sh)
+ are provided to to run on HPC clusters.)
+
+## Additional information
+
+The formulations implement non-overlapping Schwarz domain decomposition methods
+for time-harmonic acoustic and electromagnetic wave problems. Several families
+of transmission conditions are implemented: zeroth- and second-order optimized
+conditions [1-6], Padé-localized square-root conditions [7-8] and PML conditions
+[9]. Several variants of the double-sweep preconditioner [9] are also
+implemented.
+
+For more information about these methods as well as the implementation, please
+refer to [GetDDM: an Open Framework for Testing Optimized Schwarz Methods for
+Time-Harmonic Wave
+Problems](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf)
+[10].
+
+## References
+
+1. B. Després, Méthodes de Décomposition de Domaine pour les Problèmes de
+Propagation d'Ondes en Régime Harmonique. Le Théorème de Borg pour l'Equation de
+Hill Vectorielle, PhD Thesis, Paris VI University, France, 1991.
+
+2. B. Després, P. Joly and J. Roberts, A domain decomposition method for the
+harmonic Maxwell equations, Iterative methods in linear algebra (Brussels,
+1991), pp. 475-484, North-Holland, 1992.
+
+3. M. Gander, F. Magoulès and F. Nataf, Optimized Schwarz methods without
+overlap for the Helmholtz equation}, SIAM Journal on Scientific Computing,
+24(1), pp. 38-60, 2002.
+
+4. V. Dolean, M. Gander and L. Gerardo-Giorda, Optimized Schwarz methods for
+Maxwell's equations, SIAM Journal on Scientific Computing, 31(3), pp. 2193-2213,
+2009.
+
+5. A. Bendali and Y. Boubendir, Non-Overlapping Domain Decomposition Method for
+a Nodal Finite Element Method, Numerische Mathematik 103(4), pp.515-537, (2006).
+
+6. 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.
+
+7. Y. Boubendir, X. Antoine and C. Geuzaine. [A quasi-optimal non-overlapping
+domain decomposition algorithm for the Helmholtz
+equation](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_helmholtz_preprint.pdf).
+Journal of Computational Physics 231 (2), 262-280, 2012.
+
+8. M. El Bouajaji, X. Antoine and C. Geuzaine. [Approximate local
+magnetic-to-electric surface operators for time-harmonic Maxwell’s
+equations](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/osrc_maxwell_preprint.pdf).
+Journal of Computational Physics 279 241-260, 2014.
+
+9. A. Vion and C. Geuzaine. [Double sweep preconditioner for optimized Schwarz
+methods applied to the Helmholtz
+problem](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_double_sweep_preprint.pdf).
+Journal of Computational Physics 266, 171-190, 2014.
+
+10. B. Thierry, A.Vion, S. Tournier, M. El Bouajaji, D. Colignon, N. Marsic,
+X. Antoine, C. Geuzaine. [GetDDM: an Open Framework for Testing Optimized
+Schwarz Methods for Time-Harmonic Wave
+Problems](http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf).
+Computer Physics Communications 203, 309-330, 2016.
+
+----
+*Models developed by X. Antoine, Y. Boubendir, M. El Bouajaji, D. Colignon,
+@geuzaine, @marsic, @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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