Solution of the three-dimensional Helmholtz equation using ... - cerfacs
Solution of the three-dimensional Helmholtz equation using ... - cerfacs Solution of the three-dimensional Helmholtz equation using ... - cerfacs
Motivations Wave propagation modelling Solution method components: Iterative method and multigrid Solution strategy Numerical experiments Perspectives and conclusions State of the art Our approach Two-grid preconditioner for the original Helmholtz problem Intention Our intention is to use a two-level hierarchy to avoid both smoothing and coarse grid correction difficulties. Use of direct or iterative methods on coarse grid level. [Duff, Gratton, Pinel, Vasseur, 2007] Large coarse grid multigrid preconditioner method acting on the original Helmholtz problem Multigrid is not a convergent method but acts as a preconditioner for the original (unshifted) Helmholtz operator Clustered eigenspectrum of AC −1 around 1 and capture the isolated eigenvalues with Krylov subspace methods 18/27 Multigrid for geophysics applications
Motivations Wave propagation modelling Solution method components: Iterative method and multigrid Solution strategy Numerical experiments Perspectives and conclusions Outline Three-dimensional problems 1 Motivations Depth migration in geophysics 2 Wave propagation modelling Continuous problem Discrete problem 3 Solution method components: Iterative method and multigrid Classical GMRES / Restarted GMRES Multigrid 4 Solution strategy State of the art Our approach 5 Numerical experiments Three-dimensional problems 6 Perspectives and conclusions 19/27 Multigrid for geophysics applications
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Motivations<br />
Wave propagation modelling<br />
<strong>Solution</strong> method components: Iterative method and multigrid<br />
<strong>Solution</strong> strategy<br />
Numerical experiments<br />
Perspectives and conclusions<br />
State <strong>of</strong> <strong>the</strong> art<br />
Our approach<br />
Two-grid preconditioner for <strong>the</strong> original <strong>Helmholtz</strong><br />
problem<br />
Intention<br />
Our intention is to use a two-level hierarchy to avoid both<br />
smoothing and coarse grid correction difficulties.<br />
Use <strong>of</strong> direct or iterative methods on coarse grid level.<br />
[Duff, Gratton, Pinel, Vasseur, 2007]<br />
Large coarse grid multigrid preconditioner method acting on <strong>the</strong><br />
original <strong>Helmholtz</strong> problem<br />
Multigrid is not a convergent method but acts as a preconditioner<br />
for <strong>the</strong> original (unshifted) <strong>Helmholtz</strong> operator<br />
Clustered eigenspectrum <strong>of</strong> AC −1 around 1 and capture <strong>the</strong><br />
isolated eigenvalues with Krylov subspace methods<br />
18/27 Multigrid for geophysics applications
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