Hello all, I am a graduate student pursuing my Master's and I am trying to benchmark a previous work by using PETSc for solving Poisson's Equation.
I am starting off with a serial code and I am trying to keep my code modular, i.e. I generate the sparse matrix format and send it to PETSc or any other solver. So I haven't built my code from the ground up using PETSc's native data structures. I am having trouble understanding the behavior of the solver and would like your thoughts or inputs on what I can do better. I have both Dirichlet and Neumann boundary conditions and my matrix size (number of rows) is around a million but very sparse (~7 nonzeros per row), as can be expected from a finite difference discretization of Poisson's equation. I tried the methods outlined here <http://scicomp.stackexchange.com/questions/513/why-is-my-iterative-linear-solver-not-converging?rq=1> and here <http://scicomp.stackexchange.com/questions/34/how-can-i-estimate-the-condition-number-of-a-large-sparse-matrix-using-petsc>. Reverting to a 41^3 grid, I got the approximate condition number (using -ksp_monitor_singular_value -ksp_type gmres -ksp_gmres_restart 1000 -pc_type none) as ~9072, which seems pretty large. Higher matrix sizes give a larger condition number. 1) My best performing solver + preconditioner is bcgs+ilu(0) (on 1e6 grid) which solves in around 32 seconds, 196 iterations. How do I get a fix for what the lower bound on the running time could be? 2) Initially -pc_type hypre just Diverged and I was never able to use it. Looking at this thread <http://lists.mcs.anl.gov/pipermail/petsc-users/2013-October/019127.html>, I had tried the options and it no longer diverges, but the residuals reduce and hover around a constant value. How do I work with hypre to get a useful preconditioner? Initially I solve Laplace's equation, so the mesh grid size has no effect and even when I solve Poisson's equation, the spacing is carried over to the RHS, so I am pretty sure the spacing is not affecting the condition number calculation. Hope this helps. Please let me know if you might need more information. Thanking You, K.N.Ramachandran Ph: 814-441-4279
