Some puzzle about the multigrid
 

Hello every one:

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

Regards

Re: Some puzzle about the multigrid
 

The other solver is based on Gaussian elimination.

Re: Some puzzle about the multigrid
 

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

Re: Some puzzle about the multigrid
 

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.

Re: Some puzzle about the multigrid
 

what about the computational time, is it fast also

Re: Some puzzle about the multigrid
 

>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).

Re: Some puzzle about the multigrid
 

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