The reviewer said: "direct methods are useless for realistic problems". Unthinking prejudice?
Maybe I will just compare the performance of the non-compact iterative version to the compact direct one and show that it is not that bad. Thanks for the help. On Wed, Apr 1, 2015 at 1:24 PM, Matthew Knepley <[email protected]> wrote: > On Wed, Apr 1, 2015 at 11:07 AM, bichinhoverde < > [email protected]> wrote: > >> The system I am trying to solve is a 2D Poisson equation, but split into >> 5 1D equations. Something like this: >> >> p_xx + p_yy = f >> p_xx - d(p_x)/dx = 0 >> p_yy - d(p_y)/dy = 0 >> p_x - d(p)/dx = 0 >> p_y - d(p)/dy = 0 >> >> If I use standard finite differences, it works fine with gmres and >> jacobi. But when I switch to compact finite differences, only the direct >> solver works. >> >> It is on a staggered mesh, so p, p_xx and p_yy are on the cell center and >> p_x and p_y are on the edges. >> >> I recently submitted a paper and the reviewer complained about the direct >> linear solver. So I wanted to do a performance comparison. >> > > I am not sure why the direct solver is a problem, other than > > unthinking prejudice. > > If you want to use an iterative solver here, you will likely need to use > PCFIELDSPLIT since you have saddle-point > structure from the constraints (I think). > > Thanks, > > Matt > > >> On Wed, Apr 1, 2015 at 12:58 PM, Matthew Knepley <[email protected]> >> wrote: >> >>> On Wed, Apr 1, 2015 at 10:51 AM, bichinhoverde < >>> [email protected]> wrote: >>> >>>> I have a linear system which I can easily solve using the Pardiso >>>> library, which is a direct solver. But when I try Petsc, the solver does >>>> not converge. It reduces the norm a little but then gets stuck. >>>> >>>> I tried several combinations of pc_type and ksp_type. It seems that >>>> pc=jacobi is better, since my linear system does not have the diagonal >>>> element in some rows. >>>> >>>> Is there some advice you can give me? Some way to analyse the matrix >>>> and find out why it does not work? >>>> >>> >>> Without knowing anything about the system, there is nothing you can say. >>> >>> Why do you want to change from using a direct solver? >>> >>> Have you looked in the literature for iterative solvers that work on >>> this problem? >>> >>> Thanks, >>> >>> Matt >>> >>> -- >>> What most experimenters take for granted before they begin their >>> experiments is infinitely more interesting than any results to which their >>> experiments lead. >>> -- Norbert Wiener >>> >> >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener >
