GetDDM

An Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems

GetDDM1 combines GetDP and Gmsh to solve large scale finite element problems using optimized Schwarz domain decomposition methods.

Examples for time-harmonic acoustic and electromagnetic wave problems implement several families of transmission conditions: zeroth- and second-order optimized conditions2-7, Padé-localized square-root conditions8-9 and PML conditions10. Several variants of the double-sweep preconditioner10 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.

Quick start

  1. Download the precompiled ONELAB software bundle for Windows, Linux or macOS.
  2. Launch the app
  3. Open models/GetDDM/main.pro
  4. Press Run

Parallel computations

  1. Download the ONELAB source code
  2. Compile GetDP and Gmsh with MPI support
  3. Run the models on a computer cluster with MPI, e.g. the waveguide3d model on 100 CPUs, using: 
    mpirun -np 100 gmsh -setnumber N_DOM 100 waveguide3d.geo -
mpirun -np 100 getdp -setnumber N_DOM 100 waveguide3d.pro -solve DDM

The actual commands will depend on your particular MPI setup. Sample scripts for SLURM and PBS schedulers are provided.

References

  1. 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. Computer Physics Communications 203, 309-330, 2016.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. A. Bendali and Y. Boubendir, Non-Overlapping Domain Decomposition Method for a Nodal Finite Element Method, Numerische Mathematik 103(4), pp.515-537, (2006).
  7. 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.
  8. Y. Boubendir, X. Antoine and C. Geuzaine. A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. Journal of Computational Physics 231 (2), 262-280, 2012.
  9. 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 279 241-260, 2014.
  10. 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.

Sponsors

GetDDM development was funded in part by the Belgian Science Policy (IAP P6/21 and P7/02), the Belgian French Community (ARC 09/14-02 and 15/19-03), 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).