A Geometric Multigrid Preconditioner for the Solution of the Helmholtz Equation in Three-Dimensional Heterogeneous Media on Massively Parallel Computers

  • H. Calandra
  • S. Gratton
  • X. VasseurEmail author
Part of the Geosystems Mathematics book series (GSMA)


We consider the numerical simulation of acoustic wave propagation in three-dimensional heterogeneous media as occurring in seismic exploration. We focus on forward Helmholtz problems written in the frequency domain, since this setting is known to be particularly challenging for modern iterative methods. The geometric multigrid preconditioner proposed by Calandra et al. (Numer Linear Algebra Appl 20:663–688, 2013) is considered for the approximate solution of the Helmholtz equation at high frequencies in combination with dispersion minimizing finite difference methods. We present both a strong scalability study and a complexity analysis performed on a massively parallel distributed memory computer. Numerical results demonstrate the usefulness of the algorithm on a realistic three-dimensional application at high frequency.


Finite Difference Scheme Multigrid Method Perfectly Match Layer Acoustic Imaging Krylov Subspace Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank TOTAL for the financial support over the past years. They also would like to acknowledge GENCI (Grand Equipement National de Calcul Intensif) for the dotation of computing hours on the IBM BG/Q computer at IDRIS, France. This work was granted access to the HPC resources of IDRIS under allocation 2015065068 and 2016065068 made by GENCI.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.TOTAL E&P Research and Technology USAHoustonUSA
  2. 2.INPT-IRITUniversity of Toulouse and ENSEEIHTToulouse Cedex 7France
  3. 3.ISAE-SUPAEROToulouse Cedex 4France

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