<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Hi <div class=""><br class=""></div><div class="">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. </div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">A typical problem I’m trying has 16906 rows and 16906 cols. The message printed out by ksp_view is as following:</div><div class=""><br class=""></div><div class=""><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class="">KSP Object: 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: gmres</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> GMRES: happy breakdown tolerance 1e-30</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> maximum iterations=10000, initial guess is zero</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> left preconditioning</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> using PRECONDITIONED norm type for convergence test</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class="">PC Object: 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: ksp</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> KSP and PC on KSP preconditioner follow</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> ---------------------------------</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> KSP Object: (ksp_) 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: gmres</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> GMRES: happy breakdown tolerance 1e-30</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> maximum iterations=10000, initial guess is zero</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> left preconditioning</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> using PRECONDITIONED norm type for convergence test</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> PC Object: (ksp_) 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: ilu</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> ILU: out-of-place factorization</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> 0 levels of fill</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> tolerance for zero pivot 2.22045e-14</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> matrix ordering: natural</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> factor fill ratio given 1, needed 1</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> Factored matrix follows:</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> Mat Object: 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: seqaij</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> rows=16906, cols=16906</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> package used to perform factorization: petsc</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total: nonzeros=988540, allocated nonzeros=988540</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total number of mallocs used during MatSetValues calls =0</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> using I-node routines: found 7582 nodes, limit used is 5</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> linear system matrix = precond matrix:</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> Mat Object: 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: seqaij</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> rows=16906, cols=16906</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total: nonzeros=988540, allocated nonzeros=988540</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total number of mallocs used during MatSetValues calls =0</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> using I-node routines: found 7582 nodes, limit used is 5</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> ---------------------------------</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> linear system matrix = precond matrix:</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> Mat Object: 1 MPI processes</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> type: seqaij</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> rows=16906, cols=16906</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total: nonzeros=988540, allocated nonzeros=988540</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> total number of mallocs used during MatSetValues calls =0</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Menlo;" class=""><span style="font-variant-ligatures: no-common-ligatures" class=""> using I-node routines: found 7582 nodes, limit used is 5</span></div></div><div class=""><span style="font-variant-ligatures: no-common-ligatures" class=""><br class=""></span></div><div class="">Could anyone give me any suggestion please?</div><div class=""><br class=""></div><div class="">Thanks</div><div class="">Jie Cheng</div></body></html>