> I do not have an inner inner solve, I just use a single SparseILU<double> > initialized with system_matrix.block(0,0) to approximate its inverse. It is > the trick used in step-22.
You might get SparseILU(0) to work with an inner solver like in step-56. It might not be fast, but it should at least work. > Looks like the direct solver is the best choice except for multigrid. Really? For the medium mesh ILU is a lot faster (16s vs 237s) and uses less memory. If you extrapolate from there, large problems will not only require a lot of memory but also be slower. This is because a full LU factorization takes O(n^3) operations in general. > The > size of problem will certainly be limited on a single machine because of the > memory usage. But what if I parallelize my code using distributed-memory? There are special direct solvers that work okay for medium sized problems in parallel. > Does dealii have a parallel version of direct solver? My ultimate problem > size will have less than 10 million dofs. The cluster I have access to has > 16G memory on each node, I can probably use 64 nodes or even more. Will I be > able to solve such a problem using direct solver for > system_matrix.block(0,0)? You can try parallel direct solvers like Mumps, SuperLU, or KLU with interfaces exposed through PETSc or Trilinos. I assume they will work reasonable well up to that size. > I have no experience in multigrid. Forgive me if I am asking the wrong > question: is algebraic multigrid method a black box comparing to the > geometric one? By black box I mean it requires no additional information > other than the matrix itself hence no additional coding. Correct. See step-55 or step-40 for example. The problem is tuning AMG parameters to get good performance especially if your problem is not Laplace-like. -- Timo Heister http://www.math.clemson.edu/~heister/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
