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<p style="margin-top:0;margin-bottom:0">Sorry, just to clarify, in the second case I see several *inner* iterations, even though I'm using LU on a supposedly exact Schur complement as the preconditioner for the Schur system.</p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of Cotter, Colin J via petsc-users <petsc-users@mcs.anl.gov><br>
<b>Sent:</b> 18 March 2019 20:14:48<br>
<b>To:</b> petsc-users@mcs.anl.gov<br>
<b>Subject:</b> [petsc-users] Confusing Schur preconditioner behaviour</font>
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<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Dear petsc-users,</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
I'm solving a 2x2 block system, for which I can construct the Schur complement analytically (through compatible FEM stuff),</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
which I can pass as the preconditioning matrix.</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
<br>
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
When using gmres on the outer iteration, and preonly+lu on the inner iterations with a Schur complement preconditioner,</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
I see convergence in 1 iteration as expected. However, when I set gmres+lu on the inner iteration for S, I see several iterations.</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
<br>
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
This seems strange to me, as the first result seems to confirm that I have an exact Schur complement, but the second result</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
implies not.</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
What could be going on here?</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
<br>
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
I've appended output to the bottom of this message, first the preonly+lu and then for gmres+lu.</p>
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<br>
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
all the best</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
--Colin</p>
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<br>
</p>
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</p>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Linear firedrake_0_fieldsplit_1_ solve converged due to CONVERGED_ITS iterations 1</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Residual norms for firedrake_0_ solve.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
0 KSP preconditioned resid norm 4.985448866758e+00 true resid norm 1.086016610848e-03 ||r(i)||/||b|| 1.000000000000e+00</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Linear firedrake_0_fieldsplit_1_ solve converged due to CONVERGED_ITS iterations 1</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
1 KSP preconditioned resid norm 1.245615753306e-13 true resid norm 2.082000915439e-14 ||r(i)||/||b|| 1.917098591903e-11</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: gmres</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
happy breakdown tolerance 1e-30</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-07, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using PRECONDITIONED norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: fieldsplit</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
FieldSplit with Schur preconditioner, factorization FULL</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Preconditioner for the Schur complement formed from A11</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split info:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split number 0 Defined by IS</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split number 1 Defined by IS</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP solver for A00 block</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 1.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix = precond matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP solver for S = A11 - A10 inv(A00) A01 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 5.09173</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=1360836, allocated nonzeros=1360836</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix followed by preconditioner matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: schurcomplement</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Schur complement A11 - A10 inv(A00) A01</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A11</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=267264, allocated nonzeros=267264</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A10</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=73728, allocated nonzeros=73728</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP of A00</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 1.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix = precond matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A01</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=73728, allocated nonzeros=73728</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=267264, allocated nonzeros=267264</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix followed by preconditioner matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: nest</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=21504, cols=21504</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Matrix object: </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type=nest, rows=2, cols=2 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
MatNest structure: </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(0,0) : type=seqaij, rows=15360, cols=15360 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(0,1) : type=seqaij, rows=15360, cols=6144 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(1,0) : type=seqaij, rows=6144, cols=15360 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(1,1) : type=seqaij, rows=6144, cols=6144 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: nest</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=21504, cols=21504</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Matrix object: </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type=nest, rows=2, cols=2 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
MatNest structure: </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(0,0) : prefix="firedrake_0_fieldsplit_1_", type=seqaij, rows=15360, cols=15360 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(0,1) : type=seqaij, rows=15360, cols=6144 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(1,0) : type=seqaij, rows=6144, cols=15360 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
(1,1) : prefix="firedrake_0_fieldsplit_0_", type=seqaij, rows=6144, cols=6144 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
<br>
</div>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
=====</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
<br>
</p>
<p style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
</p>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Residual norms for firedrake_0_fieldsplit_1_ solve.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
0 KSP preconditioned resid norm 8.819238435108e-02 true resid norm 1.797571993221e-01 ||r(i)||/||b|| 1.000000000000e+00</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
1 KSP preconditioned resid norm 1.025167319984e-02 true resid norm 3.340583874349e-02 ||r(i)||/||b|| 1.858386694356e-01</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
2 KSP preconditioned resid norm 1.235104644359e-03 true resid norm 8.148396804822e-03 ||r(i)||/||b|| 4.533001646417e-02</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
3 KSP preconditioned resid norm 1.624748553125e-04 true resid norm 1.612221957927e-03 ||r(i)||/||b|| 8.968886720573e-03</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
4 KSP preconditioned resid norm 2.233373761266e-05 true resid norm 3.292437172839e-04 ||r(i)||/||b|| 1.831602397710e-03</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
5 KSP preconditioned resid norm 1.895393184017e-06 true resid norm 4.091207337005e-05 ||r(i)||/||b|| 2.275962994770e-04</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
6 KSP preconditioned resid norm 1.699212495729e-07 true resid norm 3.851173419652e-06 ||r(i)||/||b|| 2.142430697728e-05</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Linear firedrake_0_fieldsplit_1_ solve converged due to CONVERGED_RTOL iterations 6</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: fieldsplit</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
FieldSplit with Schur preconditioner, factorization FULL</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Preconditioner for the Schur complement formed from A11</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split info:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split number 0 Defined by IS</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Split number 1 Defined by IS</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP solver for A00 block</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 1.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix = precond matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP solver for S = A11 - A10 inv(A00) A01 </div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: gmres</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
happy breakdown tolerance 1e-30</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using PRECONDITIONED norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 5.09173</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=1360836, allocated nonzeros=1360836</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix followed by preconditioner matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: schurcomplement</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Schur complement A11 - A10 inv(A00) A01</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A11</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=15360</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=267264, allocated nonzeros=267264</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A10</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=15360, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=73728, allocated nonzeros=73728</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 5120 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP of A00</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
KSP Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: preonly</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
maximum iterations=10000, initial guess is zero</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
left preconditioning</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using NONE norm type for convergence test</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
PC Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: lu</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
out-of-place factorization</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
tolerance for zero pivot 2.22045e-14</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
matrix ordering: nd</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
factor fill ratio given 5., needed 1.</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Factored matrix follows:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
package used to perform factorization: petsc</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
linear system matrix = precond matrix:</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
Mat Object: (firedrake_0_fieldsplit_0_) 1 MPI processes</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
type: seqaij</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
rows=6144, cols=6144</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total: nonzeros=18432, allocated nonzeros=18432</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
total number of mallocs used during MatSetValues calls =0</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
using I-node routines: found 2048 nodes, limit used is 5</div>
<div style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">
A01</div>
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Mat Object: 1 MPI processes</div>
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type: seqaij</div>
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rows=6144, cols=15360</div>
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total: nonzeros=73728, allocated nonzeros=73728</div>
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total number of mallocs used during MatSetValues calls =0</div>
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using I-node routines: found 2048 nodes, limit used is 5</div>
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Mat Object: (firedrake_0_fieldsplit_1_) 1 MPI processes</div>
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type: seqaij</div>
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rows=15360, cols=15360</div>
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total: nonzeros=267264, allocated nonzeros=267264</div>
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total number of mallocs used during MatSetValues calls =0</div>
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using I-node routines: found 5120 nodes, limit used is 5</div>
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linear system matrix followed by preconditioner matrix:</div>
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Mat Object: (firedrake_0_) 1 MPI processes</div>
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type: nest</div>
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rows=21504, cols=21504</div>
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Matrix object: </div>
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type=nest, rows=2, cols=2 </div>
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MatNest structure: </div>
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(0,0) : type=seqaij, rows=15360, cols=15360 </div>
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(0,1) : type=seqaij, rows=15360, cols=6144 </div>
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(1,0) : type=seqaij, rows=6144, cols=15360 </div>
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(1,1) : type=seqaij, rows=6144, cols=6144 </div>
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Mat Object: (firedrake_0_) 1 MPI processes</div>
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type: nest</div>
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rows=21504, cols=21504</div>
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Matrix object: </div>
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type=nest, rows=2, cols=2 </div>
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MatNest structure: </div>
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(0,0) : prefix="firedrake_0_fieldsplit_1_", type=seqaij, rows=15360, cols=15360 </div>
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(0,1) : type=seqaij, rows=15360, cols=6144 </div>
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(1,0) : type=seqaij, rows=6144, cols=15360 </div>
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(1,1) : prefix="firedrake_0_fieldsplit_0_", type=seqaij, rows=6144, cols=6144 </div>
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