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<img src="marmousi.png" alt="">
</div>
<h1>Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems</h1>
<h1>An Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic
Wave Problems</h1>
<p>
GetDDM combines <a href="http://getdp.info">GetDP</a>
and <a href="http://gmsh.info">Gmsh</a> to solve large scale finite element
problems using optimized Schwarz domain decomposition methods.
GetDDM<a href="#1"><sup>1</sup></a> combines <a href="http://getdp.info">GetDP</a>
and <a href="http://gmsh.info">Gmsh</a> to solve large scale finite element
problems using optimized Schwarz domain decomposition methods.
</p>
<p>
<a href="https://gitlab.onelab.info/doc/models/wikis/Domain-decomposition-methods-for-waves">Examples
for time-harmonic acoustic and electromagnetic wave problems</a> implement
several families of transmission conditions: zeroth- and second-order
optimized conditions<a href="#2"><sup>2-7</sup></a>, Padé-localized
square-root conditions<a href="#8"><sup>8-9</sup></a> and PML
conditions<a href="#10"><sup>10</sup></a>. Several variants of the
double-sweep preconditioner<a href="#10"><sup>10</sup></a> are also
implemented.
</p>
<p>
For more information about these methods as well as the implementation, please
refer
to <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf">GetDDM:
an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave
Problems</a>.
</p>
<h2>Quick start</h2>
......@@ -63,72 +80,55 @@ problems using optimized Schwarz domain decomposition methods.
mpirun -np 100 getdp models/GetDDM/waveguide3d.pro -solve DDM
</pre>
The actual commands will depend on your particular MPI setup. Sample
scripts for SLURM and PBS schedulers are also available.
scripts
for <a href="https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_slurm.sh">SLURM</a>
and <a href="https://gitlab.onelab.info/doc/models/tree/master/DDMWaves/run_pbs.sh">PBS</a>
schedulers are also available.
</ol>
(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.)
for time-harmonic acoustic and electromagnetic wave problems. See 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].
<h2>References</h2>
<div class="small">
<ol class="small">
<li>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.
<li>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.
<li>M. Gander, F. Magoulès and F. Nataf, Optimized Schwarz methods without
<li><a name="1"></a>B. Thierry, A.Vion, S. Tournier, M. El Bouajaji,
D. Colignon, N. Marsic, X. Antoine,
C. Geuzaine. <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf">GetDDM:
an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic
Wave Problems</a>. Computer Physics Communications 203, 309-330, 2016.
<li><a name="2"></a>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.
<li><a name="3"></a>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.
<li><a name="4"></a>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.
<li>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.
<li>A. Bendali and Y. Boubendir, Non-Overlapping Domain Decomposition Method
for a Nodal Finite Element Method, Numerische Mathematik 103(4),
pp.515-537, (2006).
<li>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.
<li>Y. Boubendir, X. Antoine and
<li><a name="5"></a>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.
<li><a name="6"></a>A. Bendali and Y. Boubendir, Non-Overlapping Domain
Decomposition Method for a Nodal Finite Element Method, Numerische
Mathematik 103(4), pp.515-537, (2006).
<li><a name="7"></a>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.
<li><a name="8"></a>Y. Boubendir, X. Antoine and
C. Geuzaine. <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_helmholtz_preprint.pdf">A
quasi-optimal non-overlapping domain decomposition algorithm for the
Helmholtz equation</a>. Journal of Computational Physics 231 (2),
262-280, 2012.
<li>M. El Bouajaji, X. Antoine and
<li><a name="9"></a>M. El Bouajaji, X. Antoine and
C. Geuzaine. <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/osrc_maxwell_preprint.pdf">Approximate
local magnetic-to-electric surface operators for time-harmonic Maxwell's
equations</a>. Journal of Computational Physics 279 241-260, 2014.
<li>A. Vion and
<li><a name="10"></a>A. Vion and
C. Geuzaine. <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/ddm_double_sweep_preprint.pdf">
Double sweep preconditioner for optimized Schwarz methods applied to the
Helmholtz problem</a>. Journal of Computational Physics 266, 171-190,
2014.
<li>B. Thierry, A.Vion, S. Tournier, M. El Bouajaji, D. Colignon, N. Marsic,
X. Antoine,
C. Geuzaine. <a href="http://www.montefiore.ulg.ac.be/~geuzaine/preprints/getddm_preprint.pdf">GetDDM:
an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic
Wave Problems</a>. Computer Physics Communications 203, 309-330, 2016.
</ol>
</div>
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