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Some puzzle about the multigrid

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Old   May 7, 2007, 05:37
Default Some puzzle about the multigrid
  #1
ztdep
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Hello every one:

I want to know what advantage does the multigrd have compared to other solver.

Regards
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Old   May 7, 2007, 11:10
Default Re: Some puzzle about the multigrid
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ofc
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The other solver is based on Gaussian elimination.
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Old   May 8, 2007, 02:34
Default Re: Some puzzle about the multigrid
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Rami
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It is faster than other methods - convergence rate O(n). See the following links: CFD-Wiki http://www.cfd-online.com/Wiki/Multigrid_methods and mainly Wikipedia http://en.wikipedia.org/wiki/Multigrid_method
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Old   May 10, 2007, 10:59
Default Re: Some puzzle about the multigrid
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john deas
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It allows you to speed-up a resolution. Multigrid is not a solver per se, it is a method that you use with a solver to accelerate convergence. For example, you combine gaussian elimination with multigrid.
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Old   May 10, 2007, 19:54
Default Re: Some puzzle about the multigrid
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ztdep
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what about the computational time, is it fast also

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Old   May 11, 2007, 08:51
Default Re: Some puzzle about the multigrid
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Mani
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>what about the computational time, is it fast also

This is actually a good question, rarely asked and addressed. A multigrid iteration reduces the residual more effectively than a single-grid iteration. Duh! You're also doing more work in a multigrid cycle. What's the trade-off?

Ideally, multigrid is much more effective at relatively modest additional effort per iteration. Additional work essentially consists of solutions on coarser grids (for example dividing the number of grid cells by 8 on each grid level in 3D (4 in 2D)). A crude assessment will tell you, for example, that a multigrid V-cycle on 3 grid levels, with factor 0.5 coarsening in all three directions, requires only about 25%-30% more work than a single-grid iteration on the finest grid. The benefit, however, is that multigrid iterations effectively reduce residuals of large wave-length, which can take forever to be reduced with single-grid iterations. So the answer is: "yes, multigrid requires less wall-clock time". That's the ideal situation, anyway. In practice, the benefit depends on a number of factors, such as application (type of flow, geometry) and grid size (a very large grid that allows for a lot of grid levels will obviously benefit more than a computation on 2x2x2 cells).
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Old   May 13, 2007, 01:52
Default Re: Some puzzle about the multigrid
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ztdep
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Thank you very much for your excellent feedback. Would you please provide some good free reference or code so as to make it easy to start from. regards
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