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implementation of agglomeration multigrid

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Old   February 27, 2008, 21:27
Default implementation of agglomeration multigrid
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I am currently implementing multigrid for unstructured grids (2d). I had successfully implemented a defect correction technique and obtained a good convergence rate for higher order solutions. Now, I am in process of implementing the agglomeration multigrid technique. I have some doubts regarding the treatment of coarser grids

1) How to determine the grid spacing (h) of coarser grid (arbitrary polygon) ? Or, how to decide the timestep to take in the coarser grid?

2) Restriction operation is done by injection (agglomeration). If I do a linear interpolation for prolongation, will it give a good convergence? Will the discontinuity at the coarse grid affect the convergence in the fine grid? I saw some implicit methods for prolongation. I was wondering if I should put the effort in doing that.

3) In the coarse grids can I have a first order approximation for convective fluxes and second order for viscous fluxes? I guess it would be more stable that way, and permit a relaxes time stepping in coarser grids.

4) Is there explicit algebraic multigrid technique for finite volume methods (without forming a big matrix). If so, can you give a reference?

Thanks in advance for your clarifications.


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