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 Three-dimensional problems Iterative method on the coarse grid Experiments with the same amount of memory per processor FGMRES(5) preconditioned by a Two grid cycle Grid procs 0 30 60 120 240 480 It 4 5 8 128 3 2 Time (s) 95.63 131.10 217.10 Time/it (s) 23.90 26.22 27.13 It 5 6 5 10 256 3 16 Time (s) 129.72 175.67 147.17 295.99 Time/it (s) 25.94 29.27 29.43 29.60 It 6 18 11 10 20 512 3 128 Time (s) 155.39 519.92 318.15 290.54 579.05 Time/it (s) 25.89 28.88 28.92 29.05 28.95 It 9 74 60 41 33 64 1024 3 1024 Time (s) 270.58 2240.08 1823.02 1252.53 1013.75 1942.21 Time/it (s) 30.06 30.27 30.38 30.55 30.72 30.35 k Coarse grid solver GMRES(10) preconditioned by one Gauss-Seidel cycle. 24/27 Multigrid for geophysics applications
Motivations Wave propagation modelling Solution method components: Iterative method and multigrid Solution strategy Numerical experiments Perspectives and conclusions Three-dimensional problems History of convergence: 1024 3 grid with k = 480 25/27 Multigrid for geophysics applications
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- Page 3 and 4: Motivations Wave propagation modell
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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 />
Three-<strong>dimensional</strong> problems<br />
Iterative method on <strong>the</strong> coarse grid<br />
Experiments with <strong>the</strong> same amount <strong>of</strong> memory per processor<br />
FGMRES(5) preconditioned by a Two grid cycle<br />
Grid procs 0 30 60 120 240 480<br />
It 4 5 8<br />
128 3 2 Time (s) 95.63 131.10 217.10<br />
Time/it (s) 23.90 26.22 27.13<br />
It 5 6 5 10<br />
256 3 16 Time (s) 129.72 175.67 147.17 295.99<br />
Time/it (s) 25.94 29.27 29.43 29.60<br />
It 6 18 11 10 20<br />
512 3 128 Time (s) 155.39 519.92 318.15 290.54 579.05<br />
Time/it (s) 25.89 28.88 28.92 29.05 28.95<br />
It 9 74 60 41 33 64<br />
1024 3 1024 Time (s) 270.58 2240.08 1823.02 1252.53 1013.75 1942.21<br />
Time/it (s) 30.06 30.27 30.38 30.55 30.72 30.35<br />
k<br />
Coarse grid solver GMRES(10) preconditioned by one<br />
Gauss-Seidel cycle.<br />
24/27 Multigrid for geophysics applications
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