<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><font face="Verdana" size="4">I tried to solve S with game and use svd on the coarse grid, then I got the error: Arugments are incompatible, Zero diagonal on row 0.</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">In my opinion, S should be rank-efficient, but not elliptic.</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Best regards,</font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 20, 2025, at 10:07, Matthew Knepley <knepley@gmail.com> wrote:</div><br class="Apple-interchange-newline"><div><meta charset="UTF-8"><div dir="ltr" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div dir="ltr">On Thu, Jun 19, 2025 at 9:18 PM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn">hexiaofeng@buaa.edu.cn</a>> wrote:</div><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Hello,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Here are the outputs with svd:</font></div><div><font face="Verdana" size="4"><br></font></div><div><div><font face="Verdana" size="4">0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_1_ solve did not converge due to DIVERGED_PC_FAILED</font></div></div></div></blockquote><div><br></div><div>You are running ILU(0) on your Schur complement, but it looks like it is rank-deficient. You will have to use something that works for that (like maybe GAMG again with SVD on the coarse grid). Is S elliptic?</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><div><font face="Verdana" size="4">iterations 0</font></div><div><font face="Verdana" size="4"> PC failed due to SUBPC_ERROR </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4">Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0</font></div><div><font face="Verdana" size="4"> PC failed due to SUBPC_ERROR </font></div><div><font face="Verdana" size="4">KSP Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: cg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=200, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using UNPRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4">PC Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: fieldsplit</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>FieldSplit with Schur preconditioner, blocksize = 1, factorization FULL</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split info:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split number 0 Defined by IS</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split number 1 Defined by IS</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP solver for A00 block</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gamg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type is MULTIPLICATIVE, levels=2 cycles=v</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Cycles per PCApply=1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Using externally compute Galerkin coarse grid matrices</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>GAMG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold for dropping small values in graph on each level = </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold scaling factor for each level not specified = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>AGG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Symmetric graph false</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number of levels to square graph 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number smoothing steps 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Complexity: grid = 1.00222</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Coarse grid solver -- level -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=1, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: svd</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>All singular values smaller than 1e-12 treated as zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Provided essential rank of the matrix 0 (all other eigenvalues are zeroed)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using nonscalable MatPtAP() implementation</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Down solver (pre-smoother) on level 1 -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: chebyshev</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalue estimates used: min = 0.0998145, max = 1.09796</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimate via gmres min 0.00156735, max 0.998145</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gmres</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>happy breakdown tolerance 1e-30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-12, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using PRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>estimating eigenvalues using noisy right hand side</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=2, nonzero initial guess</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Up solver (post-smoother) same as down solver (pre-smoother)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP solver for S = A11 - A10 inv(A00) A01 </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_sub_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_sub_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: ilu</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>out-of-place factorization</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>0 levels of fill</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerance for zero pivot 2.22045e-14</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>matrix ordering: natural</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>factor fill ratio given 1., needed 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Factored matrix follows:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>package used to perform factorization: petsc</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix followed by preconditioner matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: schurcomplement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Schur complement A11 - A10 inv(A00) A01</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A11</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A10</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=48, allocated nonzeros=48</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 74 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP of A00</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gamg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type is MULTIPLICATIVE, levels=2 cycles=v</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Cycles per PCApply=1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Using externally compute Galerkin coarse grid matrices</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>GAMG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold for dropping small values in graph on each level = </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold scaling factor for each level not specified = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>AGG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Symmetric graph false</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number of levels to square graph 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number smoothing steps 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Complexity: grid = 1.00222</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Coarse grid solver -- level -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=1, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: svd</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>All singular values smaller than 1e-12 treated as zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Provided essential rank of the matrix 0 (all other eigenvalues are zeroed)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using nonscalable MatPtAP() implementation</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Down solver (pre-smoother) on level 1 -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: chebyshev</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalue estimates used: min = 0.0998145, max = 1.09796</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimate via gmres min 0.00156735, max 0.998145</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gmres</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>happy breakdown tolerance 1e-30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-12, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using PRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>estimating eigenvalues using noisy right hand side</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=2, nonzero initial guess</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Up solver (post-smoother) same as down solver (pre-smoother)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A01</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=48, allocated nonzeros=48</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 135 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=624, cols=624</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25536, allocated nonzeros=25536</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 336 nodes, limit used is 5</font></div></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Thanks,</font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><div><br></div><br id="m_-2860969419986527030lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 20, 2025, at 00:56, Mark Adams <<a href="mailto:mfadams@lbl.gov" target="_blank">mfadams@lbl.gov</a>> wrote:</div><br><div><div dir="ltr">This is what Matt is looking at:<div><br></div><div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><span style="color: rgb(80, 0, 80);"><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: lu</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">This should be svd, not lu</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">If you had used -options_left you would have caught this mistake(s)</font></div></span></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jun 19, 2025 at 8:06 AM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div dir="ltr">On Thu, Jun 19, 2025 at 7:59 AM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn" target="_blank">hexiaofeng@buaa.edu.cn</a>> wrote:</div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Hello sir, </font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">I remove the duplicated "_type", and get the same error and output.</font></div></div></blockquote><div><br></div><div>The output cannot be the same. Please send it.</div><div><br></div><div> <span class="Apple-converted-space"> </span>Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Best regards,</font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><br id="m_-2860969419986527030m_-720784505461858742m_5966237863916720487lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 19, 2025, at 19:45, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:</div><br><div><div dir="ltr">This options is wrong<div><br></div><div> -fieldsplit_0_mg_coarse_sub_pc_type_type svd</div><div><br></div><div>Notice that "_type" is repeated.</div><div><br></div><div> <span class="Apple-converted-space"> </span>Thanks,</div><div><br></div><div> <span class="Apple-converted-space"> </span>Matt</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jun 19, 2025 at 7:10 AM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn" target="_blank">hexiaofeng@buaa.edu.cn</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Dear authors,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Here are the options passed with fieldsplit preconditioner:</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">-ksp_type cg -pc_type fieldsplit -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_0_mg_coarse_sub_pc_type_type svd -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason </font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">and the output:</font></div><div><font face="Verdana" size="4"><br></font></div><div><div><font face="Verdana" size="4">0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_1_ solve did not converge due to DIVERGED_PC_FAILED iterations 0</font></div><div><font face="Verdana" size="4"> PC failed due to SUBPC_ERROR </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2</font></div><div><font face="Verdana" size="4">Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0</font></div><div><font face="Verdana" size="4"> PC failed due to SUBPC_ERROR </font></div><div><font face="Verdana" size="4">KSP Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: cg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=200, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using UNPRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4">PC Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: fieldsplit</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>FieldSplit with Schur preconditioner, blocksize = 1, factorization FULL</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split info:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split number 0 Defined by IS</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Split number 1 Defined by IS</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP solver for A00 block</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gamg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type is MULTIPLICATIVE, levels=2 cycles=v</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Cycles per PCApply=1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Using externally compute Galerkin coarse grid matrices</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>GAMG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold for dropping small values in graph on each level = </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold scaling factor for each level not specified = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>AGG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Symmetric graph false</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number of levels to square graph 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number smoothing steps 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Complexity: grid = 1.00222</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Coarse grid solver -- level -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=1, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: lu</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>out-of-place factorization</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerance for zero pivot 2.22045e-14</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using diagonal shift on blocks to prevent zero pivot [INBLOCKS]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>matrix ordering: nd</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>factor fill ratio given 5., needed 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Factored matrix follows:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>package used to perform factorization: petsc</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using nonscalable MatPtAP() implementation</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Down solver (pre-smoother) on level 1 -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: chebyshev</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalue estimates used: min = 0.0998145, max = 1.09796</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimate via gmres min 0.00156735, max 0.998145</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gmres</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>happy breakdown tolerance 1e-30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-12, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using PRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>estimating eigenvalues using noisy right hand side</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=2, nonzero initial guess</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Up solver (post-smoother) same as down solver (pre-smoother)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP solver for S = A11 - A10 inv(A00) A01 </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_1_sub_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_1_sub_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: ilu</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>out-of-place factorization</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>0 levels of fill</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerance for zero pivot 2.22045e-14</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>matrix ordering: natural</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>factor fill ratio given 1., needed 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Factored matrix follows:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>package used to perform factorization: petsc</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix followed by preconditioner matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: schurcomplement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Schur complement A11 - A10 inv(A00) A01</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A11</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A10</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=48, allocated nonzeros=48</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 74 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP of A00</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gamg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type is MULTIPLICATIVE, levels=2 cycles=v</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Cycles per PCApply=1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Using externally compute Galerkin coarse grid matrices</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>GAMG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold for dropping small values in graph on each level = </font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold scaling factor for each level not specified = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>AGG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Symmetric graph false</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number of levels to square graph 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number smoothing steps 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Complexity: grid = 1.00222</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Coarse grid solver -- level -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=1, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: lu</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>out-of-place factorization</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerance for zero pivot 2.22045e-14</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using diagonal shift on blocks to prevent zero pivot [INBLOCKS]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>matrix ordering: nd</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>factor fill ratio given 5., needed 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Factored matrix follows:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>package used to perform factorization: petsc</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=8, cols=8</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=56, allocated nonzeros=56</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using nonscalable MatPtAP() implementation</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Down solver (pre-smoother) on level 1 -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: chebyshev</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalue estimates used: min = 0.0998145, max = 1.09796</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimate via gmres min 0.00156735, max 0.998145</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gmres</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>happy breakdown tolerance 1e-30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-12, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using PRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>estimating eigenvalues using noisy right hand side</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=2, nonzero initial guess</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Up solver (post-smoother) same as down solver (pre-smoother)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: (fieldsplit_0_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=480</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25200, allocated nonzeros=25200</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 160 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>A01</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=480, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=48, allocated nonzeros=48</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 135 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=144, cols=144</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=240, allocated nonzeros=240</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>not using I-node (on process 0) routines</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=624, cols=624</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25536, allocated nonzeros=25536</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 336 nodes, limit used is 5</font></div></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Thanks,</font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><div><br></div><br id="m_-2860969419986527030m_-720784505461858742m_5966237863916720487m_-3989545582392833978lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 17, 2025, at 19:05, Mark Adams <<a href="mailto:mfadams@lbl.gov" target="_blank">mfadams@lbl.gov</a>> wrote:</div><br><div><div dir="ltr">And don't use -pc_gamg_parallel_coarse_grid_solver<div>You can use that in production but for debugging use -mg_coarse_pc_type svd</div><div>Also, use -options_left and remove anything that is not used.</div><div>(I am puzzled, I see -pc_type gamg not -pc_type fieldsplit)</div><div><br></div><div>Mark</div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jun 16, 2025 at 6:40 AM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div dir="ltr">On Sun, Jun 15, 2025 at 9:46 PM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn" target="_blank">hexiaofeng@buaa.edu.cn</a>> wrote:</div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Hello,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Here are the options and outputs:</font></div><div><font face="Verdana" size="4"><br></font></div><div><div><font face="Verdana" size="4">options:</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">-ksp_type cg -pc_type gamg -pc_gamg_parallel_coarse_grid_solver -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -fieldsplit_1_mat_schur_complement_ainv_type lump -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_0_mg_coarse_pc_type_type svd -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi -fieldsplit_1_sub_pc_type sor -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason </font></div></div></div></blockquote><div><br></div><div>This option was wrong:</div><div><br></div><div> -fieldsplit_0_mg_coarse_pc_type_type svd</div><div><br></div><div>from the output, we can see that it should have been</div><div><br></div><div> -fieldsplit_0_mg_coarse_sub_pc_type_type svd</div><div><br></div><div> <span class="Apple-converted-space"> </span>THanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><div><font face="Verdana" size="4">output:</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00</font></div><div><font face="Verdana" size="4">Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0</font></div><div><font face="Verdana" size="4"> PC failed due to SUBPC_ERROR</font></div><div><font face="Verdana" size="4">KSP Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: cg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=200, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using UNPRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4">PC Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gamg</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type is MULTIPLICATIVE, levels=2 cycles=v</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Cycles per PCApply=1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Using externally compute Galerkin coarse grid matrices</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>GAMG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold for dropping small values in graph on each level =</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Threshold scaling factor for each level not specified = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>AGG specific options</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Symmetric graph false</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number of levels to square graph 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Number smoothing steps 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Complexity: grid = 1.00176</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Coarse grid solver -- level -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10000, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (mg_coarse_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: bjacobi</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>number of blocks = 1</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: preonly</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=1, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (mg_coarse_sub_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: lu</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>out-of-place factorization</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerance for zero pivot 2.22045e-14</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using diagonal shift on blocks to prevent zero pivot [INBLOCKS]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>matrix ordering: nd</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>factor fill ratio given 5., needed 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Factored matrix follows:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=7, cols=7</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>package used to perform factorization: petsc</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=45, allocated nonzeros=45</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: seqaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=7, cols=7</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=45, allocated nonzeros=45</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=7, cols=7</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=45, allocated nonzeros=45</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using nonscalable MatPtAP() implementation</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 3 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Down solver (pre-smoother) on level 1 -------------------------------</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: chebyshev</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalue estimates used: min = 0., max = 0.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimate via gmres min 0., max 0.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>KSP Object: (mg_levels_1_esteig_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: gmres</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>happy breakdown tolerance 1e-30</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=10, initial guess is zero</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-12, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using PRECONDITIONED norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=624, cols=624</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25536, allocated nonzeros=25536</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 336 nodes, limit used is 5</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>estimating eigenvalues using noisy right hand side</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>maximum iterations=2, nonzero initial guess</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>left preconditioning</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using NONE norm type for convergence test</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>PC Object: (mg_levels_1_) 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: sor</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=624, cols=624</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25536, allocated nonzeros=25536</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 336 nodes, limit used is 5 Up solver (post-smoother) same as down solver (pre-smoother)</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>linear system matrix = precond matrix:</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>Mat Object: 1 MPI processes</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>type: mpiaij</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>rows=624, cols=624</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total: nonzeros=25536, allocated nonzeros=25536</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>total number of mallocs used during MatSetValues calls=0</font></div><div><font face="Verdana" size="4"> <span class="Apple-converted-space"> </span>using I-node (on process 0) routines: found 336 nodes, limit used is 5</font></div></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Best regards,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><br id="m_-2860969419986527030m_-720784505461858742m_5966237863916720487m_-3989545582392833978m_2839857572054762463m_-3003253161800872436lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 14, 2025, at 07:28, Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>> wrote:</div><br><div><div><div><br></div> <span class="Apple-converted-space"> </span>Matt,<div><br></div><div> Perhaps we should add options -ksp_monitor_debug and -snes_monitor_debug that turn on all possible monitoring for the (possibly) nested solvers and all of their converged reasons also? Note this is not completely trivial because each preconditioner will have to supply its list based on the current solver options for it.</div><div><br></div><div> Then we won't need to constantly list a big string of problem specific monitor options to ask the user to use.</div><div><br></div><div> <span class="Apple-converted-space"> </span>Barry</div><div><br></div><div><br></div><div><br id="m_-2860969419986527030m_-720784505461858742m_5966237863916720487m_-3989545582392833978m_2839857572054762463m_-3003253161800872436lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 13, 2025, at 9:09 AM, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:</div><br><div><div dir="ltr"><div dir="ltr">On Thu, Jun 12, 2025 at 10:55 PM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn" target="_blank">hexiaofeng@buaa.edu.cn</a>> wrote:</div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Dear authors,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">I tried<span class="Apple-converted-space"> </span><b>-pc_type game -pc_gamg_parallel_coarse_grid_solver</b><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><b>-pc_type field split -pc_fieldsplit_detect_saddle_point -fieldsplit_0_ksp_type pronely -fieldsplit_0_pc_type game -fieldsplit_0_mg_coarse_pc_type sad -fieldsplit_1_ksp_type pronely -fieldsplit_1_pc_type Jacobi _fieldsplit_1_sub_pc_type for</b> , both options got the KSP_DIVERGE_PC_FAILED error.</font></div></div></blockquote><div><br></div><div>With any question about convergence, we need to see the output of</div><div><br></div><div> <span class="Apple-converted-space"> </span>-ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason</div><div><br></div><div>and all the error output.</div><div><br></div><div> <span class="Apple-converted-space"> </span>Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font face="Verdana" size="4">Thanks,</font></div><div><font face="Verdana" size="4"><br></font></div><div><font face="Verdana" size="4">Xiaofeng</font></div><br id="m_-2860969419986527030m_-720784505461858742m_5966237863916720487m_-3989545582392833978m_2839857572054762463m_-3003253161800872436m_-8146634516906487715lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 12, 2025, at 20:50, Mark Adams <<a href="mailto:mfadams@lbl.gov" target="_blank">mfadams@lbl.gov</a>> wrote:</div><br><div><br><br style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none;"><div class="gmail_quote" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none;"><div dir="ltr" class="gmail_attr">On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div dir="ltr">On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <<a href="mailto:mfadams@lbl.gov" target="_blank">mfadams@lbl.gov</a>> wrote:</div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div>Adding this to the PETSc mailing list,</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jun 12, 2025 at 3:43 AM hexioafeng <<a href="mailto:hexiaofeng@buaa.edu.cn" target="_blank">hexiaofeng@buaa.edu.cn</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Dear Professor,</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">I hope this message finds you well.</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">I am an employee at a CAE company and a heavy user of the PETSc library. I would like to thank you for your contributions to PETSc and express my deep appreciation for your work.</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Recently, I encountered some difficulties when using PETSc to solve structural mechanics problems with Lagrange multiplier constraints. After searching extensively online and reviewing several papers, I found your previous paper titled "<b>Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics</b>" seems to be the most relevant and helpful. </font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">The stiffness matrix I'm working with,<span> </span><b>K</b>, is a block saddle-point matrix of the form (A00 A01; A10 0), where<span> </span><b>A00 is singular</b>—just as described in your paper, and different from many other articles . I have a few questions regarding your work and would greatly appreciate your insights:</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">1. Is the<span> </span><b>AMG/KKT</b><span> </span>method presented in your paper available in PETSc? I tried using<span> </span><b>CG+GAMG</b><span> </span>directly but received a<span> </span><b>KSP_DIVERGED_PC_FAILED</b><span> </span>error. I also attempted to use<span> </span><b>CG+PCFIELDSPLIT</b><span> </span>with the following options: </font></div></div></blockquote><div><br></div><div>No</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font size="4" face="Verdana"> </font></div><div><font size="4" face="Verdana"> <span> </span>-pc_type fieldsplit -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi </font></div><div><font size="4" face="Verdana"> </font></div><div><font size="4" face="Verdana"> Unfortunately, this also resulted in a<span> </span><b>KSP_DIVERGED_PC_FAILED</b><span> </span>error. Do you have any suggestions?</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">2. In your paper, you compare the method with<span> </span><b>Uzawa</b>-type approaches. To my understanding, Uzawa methods typically require A00 to be invertible. How did you handle the singularity of A00 to construct an M-matrix that is invertible?</font></div><div><font size="4" face="Verdana"><br></font></div></div></blockquote><div><br></div>You add a regularization term like A01 * A10 (like springs). See the paper or any reference to augmented lagrange or Uzawa</div><div class="gmail_quote"><br><div><br></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font size="4" face="Verdana"></font></div><div><font size="4" face="Verdana">3. Can i implement the AMG/KKT method in your paper using existing<span> </span><b>AMG APIs</b>? Implementing a production-level AMG solver from scratch would be quite challenging for me, so I’m hoping to utilize existing AMG interfaces within PETSc or other packages.</font></div><div><font size="4" face="Verdana"><br></font></div></div></blockquote><div><br></div><div>You can do Uzawa and make the regularization matrix with matrix-matrix products. Just use AMG for the A00 block.</div><div><br></div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font size="4" face="Verdana"></font></div><div><font size="4" face="Verdana">4. For saddle-point systems where A00 is singular, can you recommend any more robust or efficient solutions? Alternatively, are you aware of any open-source software packages that can handle such cases out-of-the-box?</font></div><div><font size="4" face="Verdana"><br></font></div></div></blockquote><div><br></div>No, and I don't think PETSc can do this out-of-the-box, but others may be able to give you a better idea of what PETSc can do.</div><div class="gmail_quote">I think PETSc can do Uzawa or other similar algorithms but it will not do the regularization automatically (it is a bit more complicated than just A01 * A10)</div></div></blockquote><div><br></div><div>One other trick you can use is to have</div><div><br></div><div> <span> </span>-fieldsplit_0_mg_coarse_pc_type svd</div><div><br></div><div>This will use SVD on the coarse grid of GAMG, which can handle the null space in A00 as long as the prolongation does not put it back in. I have used this for the Laplacian with Neumann conditions and for freely floating elastic problems.</div><div><br></div></div></div></blockquote><div><br></div><div>Good point.</div><div>You can also use -pc_gamg_parallel_coarse_grid_solver to get GAMG to use a on level iterative solver for the coarse grid.</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div class="gmail_quote"><div></div><div> <span> </span>Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr"><div class="gmail_quote">Thanks,</div><div class="gmail_quote">Mark<br><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div><div><font size="4" face="Verdana"></font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Thank you very much for taking the time to read my email. Looking forward to hearing from you.</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Sincerely, </font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Xiaofeng He</font></div><div><font size="4" face="Verdana">-----------------------------------------------------</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Research Engineer</font></div><div><font size="4" face="Verdana"><br></font></div><div><font size="4" face="Verdana">Internet Based Engineering, Beijing, China</font></div><div><div><br></div></div></div></blockquote></div></div></blockquote></div><div><br clear="all"></div><div><br></div><span class="gmail_signature_prefix">--<span> </span></span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div 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