Hi Toby, you can use dealii::SolverGMRES with a PETSc block matrix, even in parallel. There are many options to precondition this matrix. Block triangular or block diagonal preconditioners using the schur complement come to mind (elman, wathen, ...). I am not sure what is done in elasticity, but that works for saddle point problems arising from Stokes/Oseen/Navier-Stokes problems. For the individual blocks (inner solves) you can again use PETSc solvers and preconditioners. Also take a look at step-31 (even though it uses Trilinos).
-- Timo Heister http://num.math.uni-goettingen.de/~heister 2010/7/24 Toby D. Young <[email protected]>: > > > Greetings, > > Nothing new, in that I am trying to work with the PETSc and deal.II. Here > goes with the problem I face... > > I have a block matrix (elastic-electric equations) which look like: > > (A B) > (C D) > > where A and B are symmetric square matrices and B and C are rectangular. > Obviously I would like to solve this system; though since D is not zero > (such as in, for example, step-20) I can not use the techniques given by > the deal.II tutorial. Jaka szkoda... :-) > > (i) One option is to solve the entire matrix. This is fine for me to > start, but it seems that the PETScWrappers do not allow this type of > matrix (dealii::PETScWrappers::MPI::BlockSparseMatrix) to be passed to the > GMRES solver; for example. Can this be fixed by template argument or > instantiation in the petsc_solver.*? The use of "Blocks" is specific to > deal.II right? All PETSc "sees" is another matrix to play with... > > (ii) A second option is to compute the Schur complement using a > matrix-matrix solver, which can always be constructed, and is not too > difficult to do so (PETSc has one of these and it only needs to provide > an appropriate wrapper which would use the petsc_full_matrix class). > > Any guesses which is the way to go? (i) or (ii), both, or even a (iii)?? > > I am interested in short-term solutions (getting a quick answer before > the sun comes up tomorrow) and long term solutions (hacking and > testing and then getting a fast, stable, and resusable algorithm). > > A few words of guidance, or a pointer to the lierature, if you can, would > be greatly appreciated. > > Best, > Toby > > ----- > > Toby D. Young > Assistant Professor > > Institute of Fundamental Technological Problems > Polish Academy of Sciences > ul Adolfa Pawinskiego 5b > 02-106 Warsaw > Poland > > www: http://www.ippt.gov.pl/~tyoung > skype: stenografia > > _______________________________________________ > dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii > _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
