# Some puzzle about the multigrid

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 May 7, 2007, 05:37 Some puzzle about the multigrid #1 ztdep Guest   Posts: n/a Hello every one: I want to know what advantage does the multigrd have compared to other solver. Regards

 May 7, 2007, 11:10 Re: Some puzzle about the multigrid #2 ofc Guest   Posts: n/a The other solver is based on Gaussian elimination.

 May 8, 2007, 02:34 Re: Some puzzle about the multigrid #3 Rami Guest   Posts: n/a 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

 May 10, 2007, 10:59 Re: Some puzzle about the multigrid #4 john deas Guest   Posts: n/a 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.

 May 10, 2007, 19:54 Re: Some puzzle about the multigrid #5 ztdep Guest   Posts: n/a what about the computational time, is it fast also

 May 11, 2007, 08:51 Re: Some puzzle about the multigrid #6 Mani Guest   Posts: n/a >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).

 May 13, 2007, 01:52 Re: Some puzzle about the multigrid #7 ztdep Guest   Posts: n/a 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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