Multigrid on non-uniform grids
 

Hi

Are there any multigrid methods for a Poisson equation which have a good convergence rate on highly stretched grids (about two orders of magnitude between the largest and smallest cells)?. The stretch is in both dimensions. Whilst algebraic multigrid seems very effective for a u niform grid, it rapidly becomes very slow, until it constantly diverges after the stretch is about a single order of magnitude.

Thanks. This could save me many headaches. Jude

Re: Multigrid on non-uniform grids
 

I have had similar problems. Although I have not tried them, I have a feeling that the multigrid techniques with semi-coarsening might help.

Good luck

Re: Multigrid on non-uniform grids
 

(1). I am not using Multi-grid, so I can't comment on it. (2). But based on your message, the process diverges when the mesh stretching is high. (3). So, in this area, I would suggest that you keep the cell-to-cell size stretching ratio to 1.2 or smaller. (4). The high stretching (cell-to-cell) of mesh will generate higher errors in your numerical scheme. In addition to this truncation error, you also have a source term. The form and the distribution of this source term also will have great impact on the solution stability. (5). So, Just use more grid points, and let the computer do the hard work.

Re: Multigrid on non-uniform grids
 

Hi. I deal with highly stretched grids as well. I have found that there are several factors that can greatly influence the convergence rate, and/or cause divergence. These are: 1) the choice of the restriction and prolongation operators 2) the type of smoother used at each grid level (I use ADI-type solver on the finest grid and Gauss-Seidel and the coarser ones) 3) I found that sometimes it is not so good to have too many grid levels (that could cause divergence). Finally, I have been told (but never tried myself) that the Bi-CGStab method with multigrid as a preconditionner is very efficient.

Hope this helps. Franck