[petsc-users] Diagnosing Poisson Solver Behavior

[K. N. Ramachandran]

Sorry, some more questions.

3) Also, for Dirichlet bc, I specify the value through Identity rows, i.e.
A_ii = 1 and the rhs value would correspond to the Dirichlet condition. I
am specifying it this way for my convenience. I am aware that
MatZerosRowColumns might help here, but would keeping it this way be
detrimental?

4) Can I expect symmetric matrices to perform better, i.e. if I eliminate
Dirichlet rows? But I would still be left with Neumann boundary conditions,
where I use the second order formulation. If I used the first order
formulation and made it symmetric, would that be an advantage? I tried the
latter, but I didn't see the condition number change much.



On Sat, Oct 10, 2015 at 8:51 PM, K. N. Ramachandran <knram06 at gmail.com>
wrote:

> 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
>


Thanking You,
K.N.Ramachandran
Ph: 814-441-4279
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