[petsc-users] Krylov Method Takes Too Long to Solve
Jed Brown
jed at jedbrown.org
Fri Apr 22 16:12:15 CDT 2016
Always send the output with -log_summary when asking about performance.
Jie Cheng <chengj5 at rpi.edu> writes:
> Hi
>
> I’m implementing finite element method on nonlinear solid mechanics. The main portion of my code that involves PETSc is that in each step, the tangent stiffness matrix A is formed and the increment of the nodal degrees of freedom is solved. Standard Newton’s iteration. The problem is: when I use Krylov methods to solve the linear system, the KSPsolve process takes too long, although only 2 or 3 iterations are needed.
>
> The finite element formulation is the displacement/pressure mixed formulation, which I believe is symmetric and positive-definite. However if I pick conjugate gradient method with ICC preconditioned, PETSc gives me a -8 converged reason, which indicates a non-positive-definite matrix. After a couple of trials and errors, the only pair that works is GMRES plus PCKSP. But as I said, the KSPsolve function takes too much time.
>
> A typical problem I’m trying has 16906 rows and 16906 cols. The message printed out by ksp_view is as following:
>
> KSP Object: 1 MPI processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: ksp
> KSP and PC on KSP preconditioner follow
> ---------------------------------
> KSP Object: (ksp_) 1 MPI processes
> type: gmres
> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> GMRES: happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (ksp_) 1 MPI processes
> type: ilu
> ILU: out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> matrix ordering: natural
> factor fill ratio given 1, needed 1
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=16906, cols=16906
> package used to perform factorization: petsc
> total: nonzeros=988540, allocated nonzeros=988540
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 7582 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=16906, cols=16906
> total: nonzeros=988540, allocated nonzeros=988540
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 7582 nodes, limit used is 5
> ---------------------------------
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=16906, cols=16906
> total: nonzeros=988540, allocated nonzeros=988540
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 7582 nodes, limit used is 5
>
> Could anyone give me any suggestion please?
>
> Thanks
> Jie Cheng
-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 818 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20160422/6e01e30c/attachment-0001.pgp>
More information about the petsc-users
mailing list