Hi everyone, TL;DR: I'm trying to precondition my system which can be solved with GMRES (with increasing iteration number for increasing size) but the standard preconditioners are either increasing the number of iterations, or causing the solver not to converge.
Details: I'm trying to solve a phase-field crystal system, whose time evolution equation I'm attaching as `pfc_time_evolution.png`. By introducing auxiliary variables (`auxiliary_variables.png`), it can be written as a second-order coupled equation (`reduced_pfc_time_evolution.png`). This can be discretized in time and linearized such that the linear operator looks like `block_continuous_operator.png` with dt the timestep and theta a time-stepping discretization parameter. Finally, this can be discretized in space so that the block-form of the relevant linear operator is given by `block_discrete_operator.png`. The M blocks are mass matrices and the L blocks are Laplacian operators. The rest are some sum of Laplacians, mixed mass matrices, and nonlinear terms which couple to the fields. As a first pass, I'm trying to solve the entire matrix in one go, and this works fine using the GMRES method. However, the number of GMRES iterations increase as the number of DoFs increase, so I would like to precondition to mitigate this. It's my understanding that the AMG preconditioner is a good black-box for most problems, but when I try to use it the GMRES solver does not converge (I've set max iterations to n_dofs). Additionally, a simple Jacobi preconditioner increases the number of iterations relative to no preconditioner for two different grid sizes. Finally, the ILU preconditioner decreases the number of GMRES iterations for a small grid, but then fails to converge for a large grid. What could be going on here? This is for the entire matrix, but as an aside, if it is helpful to somehow use the block structure of the matrix to precondition (it's 3x3, so can't use Schur complement I think) I'd be interested if anyone has any tips. Thanks so much for any help! - Lucas -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/0e9c920e-42d9-4d69-bdbb-28936eb601c8n%40googlegroups.com.
