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 Multigrid Classical GMRES / Restarted GMRES Multigrid Multigrid: multiscale solver designed for elliptic operators. Main advantages: Scalable in memory, O(n) complexity for elliptic operators if n denotes the number of unknowns Smoothing reduces high frequency components of the error Coarse grid approximation handles the low frequency components Relaxation methods 1/h FINE Smoothing Smoothing FINE 1/h Restriction Interpolation 1/2h 1/2h COARSE Solve the coarse problem COARSE 1/4h Figure: Left: two-grid V-cycle, right: three-grid W-cycle 14/27 Multigrid for geophysics applications
Motivations Wave propagation modelling Solution method components: Iterative method and multigrid Solution strategy Numerical experiments Perspectives and conclusions Outline State of the art Our approach 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 15/27 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 />
Outline<br />
State <strong>of</strong> <strong>the</strong> art<br />
Our approach<br />
1 Motivations<br />
Depth migration in geophysics<br />
2 Wave propagation modelling<br />
Continuous problem<br />
Discrete problem<br />
3 <strong>Solution</strong> method components: Iterative method and multigrid<br />
Classical GMRES / Restarted GMRES<br />
Multigrid<br />
4 <strong>Solution</strong> strategy<br />
State <strong>of</strong> <strong>the</strong> art<br />
Our approach<br />
5 Numerical experiments<br />
Three-<strong>dimensional</strong> problems<br />
6 Perspectives and conclusions<br />
15/27 Multigrid for geophysics applications
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