Hello, I have some concerns about the multigrid framework in PETSc.
We are trying to solve a two dimensional problem with a large variety in length
scales. The length of computational domain is in order of 1e3 m, and the width
is in 1 m, nevertheless, there is a tiny object with 1e-3 m in a corner of the
domain.
As a first thinking, we tried to solve the problem with a larger number of
uniform or non-uniform grids. However, the error of the numerical solution
increases when the number of the grid is too large. In order to test the
effect of the grid size on the solution, a domain with regular scale of 1m by
1m was tried to solve. It is found that the extreme small grid size might lead
to large variation to the exact solution. For example, the exact solution is a
linear distribution in the domain. The numerical solution is linear as similar
as the exact solution when the grid number is nx=1000 by ny=1000. However, if
the grid number is nx=10000 by ny=10000, the numerical solution varies to
nonlinear distribution which boundary is the only same as the exact solution.
The solver I used is a KSP solver in PETSc, which is set by calling :
KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr). Whether this solver
is not suitable to the system with small size grid? Or, whether the problem
crossing 6 orders of length scale is solvable with only one level grid system
when the memory is enough for large matrix? Since there is less coding work for
one level grid size, it would be easy to implement the solver.
I did some research work on the website and found the slides by Barry on
http://www.mcs.anl.gov/petsc/petsc-2/documentation/tutorials/Columbia04/DDandMultigrid.pdf
It seems that the multigrid framework in PETSc is a possible approach to our
problem. We are thinking to turn to the multigrid framework in PETSc to solve
the problem. However, before we dig into it, there are some issues confusing
us. It would be great if we can get any suggestion from you:
1 Whether the multigrid framework can handle the problem with a large variety
in length scales (up to 6 orders)? Is DMMG is the best tool for our problem?
2 The coefficient matrix A and the right hand side vector b were created for
the finite difference scheme of the domain and solved by KSP solver (call
KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr)). Is it easy to
immigrate the created Matrix A and Vector b to the multigrid framework?
3 How many levels of the subgrid are needed to obtain a solution close enough
to the exact solution for a problem with 6 orders in length scale?
-------------- next part --------------
An HTML attachment was scrubbed...
URL:
<http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110206/cc455ed1/attachment.htm>
