Abstract:
In this paper we address the solution of three-dimensional heterogeneous Helmholtz problems discretized with compact fourth-order finite difference methods with application to acoustic waveform inversion in geophysics. In this setting, the numerical simulation of wave propagation phenomena requires the approximate solution of possibly very large linear systems of equations. We propose an iterative two-grid method where the coarse grid problem is solved inexactly. A single cycle of this method is used as a variable preconditioner for a flexible Krylov subspace method. Numerical results demonstrate the usefulness of the algorithm on a realistic three-dimensional application. The proposed numerical method allows us to solve wave propagation problems with single or multiple sources even at high frequencies on a reasonable number of cores of a distributed memory cluster.
This publication is cited in the following 9 articles:
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Sun D.-L., Carpentieri B., Huang T.-Zh., Jing Ya.-F., Naveed S., “Variants of the Block-Gmres Method For Solving Linear Systems With Multiple Right-Hand Sides”, 2018 International Workshop on Computing, Electromagnetics, and Machine Intelligence (Cemi), ed. Gurel L., IEEE, 2018, 13–14
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H. Calandra, S. Gratton, X. Vasseur, Geosystems Mathematics, Modern Solvers for Helmholtz Problems, 2017, 141
Siegfried Cools, Wim Vanroose, Geosystems Mathematics, Modern Solvers for Helmholtz Problems, 2017, 53
Siegfried Cools, Pieter Ghysels, Wim van Aarle, Jan Sijbers, Wim Vanroose, “A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems”, Journal of Computational and Applied Mathematics, 283 (2015), 1
Siegfried Cools, Bram Reps, Wim Vanroose, “A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems”, Numer. Linear Algebra Appl., 21:4 (2014), 513
Sheikh A.H., Lahaye D., Vuik C., “On the Convergence of Shifted Laplace Preconditioner Combined with Multilevel Deflation”, Numer. Linear Algebr. Appl., 20:4, SI (2013), 645–662
Calandra H., Gratton S., Pinel X., Vasseur X., “An Improved Two-Grid Preconditioner for the Solution of Three-Dimensional Helmholtz Problems in Heterogeneous Media”, Numer. Linear Algebr. Appl., 20:4, SI (2013), 663–688