<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Oct 6, 2021, at 1:20 PM, Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" class="">marco.cisternino@optimad.it</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; 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 style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Hello Barry.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I tried to force the solver to start from an initial guess which is not the solution of the problem. For sake of completeness, the solution has to be a constant field.<br class="">With this initial condition, the solver iterates to a solution which is constant in the 2 sub-domains but<o:p class=""></o:p></span></div><ul type="disc" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoListParagraph" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">the constants have not the same value<o:p class=""></o:p></span></li><li class="MsoListParagraph" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">they are not close to zero (minimal norm solution)<o:p class=""></o:p></span></li><li class="MsoListParagraph" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">they are not opposite (zero-average solution over the whole domain, like 3 and -3)<o:p class=""></o:p></span></li></ul><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">After 20 CFD iterations my pressure is 32 in one sub-domain and 2.2 in the other one. And their norm is increasing.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">How can I force the solver to give me minimal norm solution, or in other words the zero constant?</span></div></div></div></blockquote><div><br class=""></div> Providing the appropriate null space should result in GMRES giving you the minimal norm solution which corresponds to the average of the solution on each domain being zero.</div><div><br class=""></div><div> For a general right hand side the residual will not decrease to zero because the right hand side is inconsistent. You can still run GMRES and the solution will converge but you will have a nonzero residual at the end (this makes the stopping criteria harder so it is useful to remove the inconsistent part of the right hand side out from the right hand side before calling GMRES.)</div><div><br class=""></div><div> Barry</div><div><br class=""></div><div><br class=""></div><div><br class=""><blockquote type="cite" class=""><div class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; 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 style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I can do it by myself, anchoring domain-by-domain the solution removing its local average, but I was wondering if the solver can do this for me.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">In some way, giving a null space made of 2 vectors (1 on dofs living in the sub-domain and zero elsewhere), I would expect a solution with zero average in the 2 sub-domains, separately, but I’m wrong, probably.<br class="">Finally, which is the closure of the problem defining the value of the constant? Zero-average condition, minimal norm condition, or none of them?<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thanks!<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Bests,<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino, PhD<br class=""></span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" class="">marco.cisternino@optimad.it</span></a><span lang="EN-GB" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">______________________<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Optimad Engineering Srl<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Via Bligny 5,<span class="Apple-converted-space"> </span></span><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30); background-color: white;" class="">Torino, Italia.</span><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30);" class=""><br class=""><span style="background-color: white;" class="">+3901119719782</span><br class=""></span><a href="http://www.optimad.it/" target="_blank" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; border: 1pt none windowtext; padding: 0cm; background-color: white;" class="">www.optimad.it</span></a><span lang="EN-GB" class=""><o:p class=""></o:p></span></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span lang="EN-US" class="">From:</span></b><span lang="EN-US" class=""><span class="Apple-converted-space"> </span>Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;" class="">bsmith@petsc.dev</a>><span class="Apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>venerdì 1 ottobre 2021 16:56<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a>><br class=""><b class="">Cc:</b><span class="Apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class="">petsc-users@mcs.anl.gov</a><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [petsc-users] Disconnected domains and Poisson equation<o:p class=""></o:p></span></div></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><br class=""><br class=""><o:p class=""></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">On Oct 1, 2021, at 6:38 AM, Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" class="">marco.cisternino@optimad.it</span></a><span lang="EN-GB" class="">> wrote:<o:p class=""></o:p></span></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thank you Barry.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I added a custom atoll = 1.0e-12 and this makes the CFD stable with all the linear solver types. CFD solution is good and pressure is a good “zero” field at every CFD iteration.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I did the same test using ASM+ILU+FGMRES(BCGS and GMRES) and the behaviour is the same.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">During some CFD iteration the residual of linear system starts slightly higher than atol and the linear solver makes some iteration (2/3 iterations) before it stops because of atol.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">The pressure is still different in the 2 sub-domains (order 1.0e-14 because of those few linear solver iterations), therefore no symmetry of the solution In the 2 sub-domains.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I think it is a matter of round-off, do you agree on this? Or do I need to take care of this difference as a symptom of something wrong?<o:p class=""></o:p></span></div></div></div></blockquote><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Yes, if the differences in the two solutions are order 1.e-14 that is very good, one cannot expect them to be identical. <br class=""><br class=""><o:p class=""></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thank you for your support.<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino<span class="apple-converted-space"> </span><o:p class=""></o:p></span></div></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span lang="EN-US" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" class="">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">bsmith@petsc.dev</span></a><span lang="EN-US" class="">><span class="apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>giovedì 30 settembre 2021 16:39<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">marco.cisternino@optimad.it</span></a><span lang="EN-US" class="">><br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">petsc-users@mcs.anl.gov</span></a><span lang="EN-US" class=""><br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [petsc-users] Disconnected domains and Poisson equation</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div></div></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> It looks like the initial solution (guess) is to round-off the solution to the linear system 9.010260489109e-14<o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">0 KSP unpreconditioned resid norm 9.010260489109e-14 true resid norm 9.010260489109e-14 ||r(i)||/||b|| 2.021559024868e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 0 KSP Residual norm 9.010260489109e-14 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 1 KSP unpreconditioned resid norm 4.918108339808e-15 true resid norm 4.918171792537e-15 ||r(i)||/||b|| 1.103450292594e-01<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 1 KSP Residual norm 4.918108339808e-15 % max 9.566256813737e-01 min 9.566256813737e-01 max/min 1.000000000000e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 2 KSP unpreconditioned resid norm 1.443599554690e-15 true resid norm 1.444867143493e-15 ||r(i)||/||b|| 3.241731154382e-02<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 2 KSP Residual norm 1.443599554690e-15 % max 9.614019380614e-01 min 7.360950481750e-01 max/min 1.306083963538e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thus the Krylov solver will not be able to improve the solution, it then gets stuck trying to improve the solution but cannot because of round off. <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">In other words the algorithm has converged (even at the initial solution (guess) and should stop immediately.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">You can use -ksp_atol 1.e-12 to get it to stop immediately without iterating if the initial residual is less than 1e-12. <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Barry<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><br class=""><br class=""><br class=""><o:p class=""></o:p></span></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">On Sep 30, 2021, at 4:16 AM, Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" class="">marco.cisternino@optimad.it</span></a><span lang="EN-GB" class="">> wrote:<o:p class=""></o:p></span></div></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Hello Barry.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">This is the output of ksp_view using fgmres and gamg. It has to be said that the solution of the linear system should be a zero values field. As you can see both unpreconditioned residual and r/b converge at this iteration of the CFD solver. During the time integration of the CFD, I can observe pressure linear solver residuals behaving in a different way: unpreconditioned residual stil converges but r/b stalls. After the output of ksp_view I add the output of ksp_monitor_true_residual for one of these iteration where r/b stalls.<br class="">Thanks,<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">KSP Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: fgmres<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> happy breakdown tolerance 1e-30<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=100, nonzero initial guess<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> right preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using UNPRECONDITIONED norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">PC Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: gamg<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type is MULTIPLICATIVE, levels=4 cycles=v<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Cycles per PCApply=1<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Using externally compute Galerkin coarse grid matrices<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> GAMG specific options<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Threshold for dropping small values in graph on each level = 0.02 0.02 <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Threshold scaling factor for each level not specified = 1.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> AGG specific options<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Symmetric graph true<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Number of levels to square graph 1<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Number smoothing steps 0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Coarse grid solver -- level -------------------------------<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_coarse_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: preonly<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=10000, initial guess is zero<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using NONE norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC Object: (mg_coarse_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: bjacobi<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> number of blocks = 1<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Local solve is same for all blocks, in the following KSP and PC objects:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_coarse_sub_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: preonly<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=1, initial guess is zero<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using DEFAULT norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC Object: (mg_coarse_sub_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: lu<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC has not been set up so information may be incomplete<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> out-of-place factorization<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerance for zero pivot 2.22045e-14<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> matrix ordering: nd<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <span class="apple-converted-space"> </span></span><span lang="FR" class="">Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-GB" class="">rows=18, cols=18<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=104, allocated nonzeros=104<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <span class="apple-converted-space"> </span></span><span lang="FR" class="">Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-GB" class="">rows=18, cols=18<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=104, allocated nonzeros=104<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Down solver (pre-smoother) on level 1 -------------------------------<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_1_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: chebyshev<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalue estimates used: min = 0., max = 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimate via gmres min 0., max 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_1_esteig_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: gmres<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> happy breakdown tolerance 1e-30<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=10, initial guess is zero<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using DEFAULT norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> estimating eigenvalues using noisy right hand side<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=2, nonzero initial guess<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using NONE norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC Object: (mg_levels_1_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: sor<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> rows=67, cols=67<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=675, allocated nonzeros=675<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Up solver (post-smoother) same as down solver (pre-smoother)<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Down solver (pre-smoother) on level 2 -------------------------------<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_2_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: chebyshev<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalue estimates used: min = 0., max = 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimate via gmres min 0., max 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_2_esteig_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: gmres<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> happy breakdown tolerance 1e-30<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=10, initial guess is zero<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using DEFAULT norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> estimating eigenvalues using noisy right hand side<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=2, nonzero initial guess<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using NONE norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC Object: (mg_levels_2_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: sor<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> rows=348, cols=348<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=3928, allocated nonzeros=3928<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Up solver (post-smoother) same as down solver (pre-smoother)<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Down solver (pre-smoother) on level 3 -------------------------------<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_3_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: chebyshev<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalue estimates used: min = 0., max = 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimate via gmres min 0., max 0.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> KSP Object: (mg_levels_3_esteig_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: gmres<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> happy breakdown tolerance 1e-30<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=10, initial guess is zero<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using DEFAULT norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> estimating eigenvalues using noisy right hand side<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> maximum iterations=2, nonzero initial guess<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> left preconditioning<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> using NONE norm type for convergence test<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> PC Object: (mg_levels_3_) 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: sor<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> rows=3584, cols=3584<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=23616, allocated nonzeros=23616<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> has attached null space<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Up solver (post-smoother) same as down solver (pre-smoother)<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> linear system matrix = precond matrix:<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Mat Object: 1 MPI processes<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> type: seqaij<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> rows=3584, cols=3584<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total: nonzeros=23616, allocated nonzeros=23616<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> total number of mallocs used during MatSetValues calls =0<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> has attached null space<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> not using I-node routines<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Pressure system has reached convergence in 0 iterations with reason 3.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 0 KSP unpreconditioned resid norm 4.798763170703e-16 true resid norm 4.798763170703e-16 ||r(i)||/||b|| 1.000000000000e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 0 KSP Residual norm 4.798763170703e-16 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 1 KSP unpreconditioned resid norm 1.648749109132e-17 true resid norm 1.648749109132e-17 ||r(i)||/||b|| 3.435779284125e-02<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 1 KSP Residual norm 1.648749109132e-17 % max 9.561792537103e-01 min 9.561792537103e-01 max/min 1.000000000000e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 2 KSP unpreconditioned resid norm 4.737880600040e-19 true resid norm 4.737880600040e-19 ||r(i)||/||b|| 9.873128619820e-04<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 2 KSP Residual norm 4.737880600040e-19 % max 9.828636644296e-01 min 9.293131521763e-01 max/min 1.057623753767e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 3 KSP unpreconditioned resid norm 2.542212716830e-20 true resid norm 2.542212716830e-20 ||r(i)||/||b|| 5.297641551371e-05<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 3 KSP Residual norm 2.542212716830e-20 % max 9.933572357920e-01 min 9.158303248850e-01 max/min 1.084652046127e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 4 KSP unpreconditioned resid norm 6.614510286263e-21 true resid norm 6.614510286269e-21 ||r(i)||/||b|| 1.378378146822e-05<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 4 KSP Residual norm 6.614510286263e-21 % max 9.950912550705e-01 min 6.296575800237e-01 max/min 1.580368896747e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 5 KSP unpreconditioned resid norm 1.981505525281e-22 true resid norm 1.981505525272e-22 ||r(i)||/||b|| 4.129200493513e-07<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> 5 KSP Residual norm 1.981505525281e-22 % max 9.984097962703e-01 min 5.316259535293e-01 max/min 1.878030577029e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Linear solve converged due to CONVERGED_RTOL iterations 5<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Ksp_monitor_true_residual output for stalling r/b CFD iteration<br class="">0 KSP unpreconditioned resid norm 9.010260489109e-14 true resid norm 9.010260489109e-14 ||r(i)||/||b|| 2.021559024868e+00<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <span class="apple-converted-space"> </span></span>0 KSP Residual norm 9.010260489109e-14 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 1 KSP unpreconditioned resid norm 4.918108339808e-15 true resid norm 4.918171792537e-15 ||r(i)||/||b|| 1.103450292594e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 1 KSP Residual norm 4.918108339808e-15 % max 9.566256813737e-01 min 9.566256813737e-01 max/min 1.000000000000e+00<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 2 KSP unpreconditioned resid norm 1.443599554690e-15 true resid norm 1.444867143493e-15 ||r(i)||/||b|| 3.241731154382e-02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 2 KSP Residual norm 1.443599554690e-15 % max 9.614019380614e-01 min 7.360950481750e-01 max/min 1.306083963538e+00<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 3 KSP unpreconditioned resid norm 6.623206616803e-16 true resid norm 6.654132553541e-16 ||r(i)||/||b|| 1.492933720678e-02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 3 KSP Residual norm 6.623206616803e-16 % max 9.764112945239e-01 min 4.911485418014e-01 max/min 1.988016274960e+00<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 4 KSP unpreconditioned resid norm 6.551896936698e-16 true resid norm 6.646157296305e-16 ||r(i)||/||b|| 1.491144376933e-02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 4 KSP Residual norm 6.551896936698e-16 % max 9.883425885532e-01 min 1.461270778833e-01 max/min 6.763582786091e+00<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 5 KSP unpreconditioned resid norm 6.222297644887e-16 true resid norm 1.720560536914e-15 ||r(i)||/||b|| 3.860282047823e-02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 5 KSP Residual norm 6.222297644887e-16 % max 1.000409371755e+00 min 4.989767363560e-03 max/min 2.004921870829e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 6 KSP unpreconditioned resid norm 6.496945794974e-17 true resid norm 2.031914800253e-14 ||r(i)||/||b|| 4.558842341106e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 6 KSP Residual norm 6.496945794974e-17 % max 1.004914985753e+00 min 1.459258738706e-03 max/min 6.886475709192e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 7 KSP unpreconditioned resid norm 1.965237342540e-17 true resid norm 1.684522207337e-14 ||r(i)||/||b|| 3.779425772373e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 7 KSP Residual norm 1.965237342540e-17 % max 1.005737762541e+00 min 1.452603803766e-03 max/min 6.923689446035e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 8 KSP unpreconditioned resid norm 1.627718951285e-17 true resid norm 1.958642967520e-14 ||r(i)||/||b|| 4.394448276241e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 8 KSP Residual norm 1.627718951285e-17 % max 1.006364278765e+00 min 1.452081813014e-03 max/min 6.930492963590e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 9 KSP unpreconditioned resid norm 1.616577677764e-17 true resid norm 2.019110946644e-14 ||r(i)||/||b|| 4.530115373837e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 9 KSP Residual norm 1.616577677764e-17 % max 1.006648747131e+00 min 1.452031376577e-03 max/min 6.932692801059e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">10 KSP unpreconditioned resid norm 1.285788988203e-17 true resid norm 2.065082694477e-14 ||r(i)||/||b|| 4.633258453698e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">10 KSP Residual norm 1.285788988203e-17 % max 1.007469033514e+00 min 1.433291867068e-03 max/min 7.029057072477e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">11 KSP unpreconditioned resid norm 5.490854431580e-19 true resid norm 1.798071628891e-14 ||r(i)||/||b|| 4.034187394623e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">11 KSP Residual norm 5.490854431580e-19 % max 1.008058905554e+00 min 1.369401685301e-03 max/min 7.361309076612e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">12 KSP unpreconditioned resid norm 1.371754802104e-20 true resid norm 1.965688920064e-14 ||r(i)||/||b|| 4.410256708163e-01<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">12 KSP Residual norm 1.371754802104e-20 % max 1.008409402214e+00 min 1.369243011779e-03 max/min 7.364721919624e+02<o:p class=""></o:p></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Linear solve converged due to CONVERGED_RTOL iterations 12<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino<span class="apple-converted-space"> </span><o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span lang="EN-US" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" class="">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">bsmith@petsc.dev</span></a><span lang="EN-US" class="">><span class="apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>mercoledì 29 settembre 2021 18:34<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">marco.cisternino@optimad.it</span></a><span lang="EN-US" class="">><br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">petsc-users@mcs.anl.gov</span></a><span lang="EN-US" class=""><br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [petsc-users] Disconnected domains and Poisson equation</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><br class=""><br class=""><br class=""><br class=""><o:p class=""></o:p></span></div></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">On Sep 29, 2021, at 11:59 AM, Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" class="">marco.cisternino@optimad.it</span></a><span lang="EN-GB" class="">> wrote:<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">For sake of completeness, explicitly building the null space using a vector per sub-domain make s the CFD runs using BCGS and GMRES more stable, but still slower than FGMRES.<o:p class=""></o:p></span></div></div></div></div></div></blockquote><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Something is strange. Please run with -ksp_view and send the output on the solver details.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><br class=""><br class=""><br class=""><br class=""><o:p class=""></o:p></span></div></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I had divergence using BCGS and GMRES setting the null space with only one constant.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thanks<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino<span class="apple-converted-space"> </span><o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span lang="EN-US" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" class="">Marco Cisternino<span class="apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>mercoledì 29 settembre 2021 17:54<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">bsmith@petsc.dev</span></a><span lang="EN-US" class="">><br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">petsc-users@mcs.anl.gov</span></a><span lang="EN-US" class=""><br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>RE: [petsc-users] Disconnected domains and Poisson equation</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thank you Barry for the quick reply.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">About the null space: I already tried what you suggest, building 2 Vec (constants) with 0 and 1 chosen by sub-domain, normalizing them and setting the null space like this<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_FALSE,nconstants,constants,&nullspace);<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">The solution is slightly different in values but it is still different in the two sub-domains.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">About the solver: I tried BCGS, GMRES and FGMRES. The linear system is a pressure system in a navier-stokes solver and only solving with FGMRES makes the CFD stable, with BCGS and GMRES the CFD solution diverges. Moreover, in the same case but with a single domain, CFD solution is stable using all the solvers, but FGMRES converges in much less iterations than the others.<o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino<span class="apple-converted-space"> </span><o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span lang="EN-US" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" class="">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">bsmith@petsc.dev</span></a><span lang="EN-US" class="">><span class="apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>mercoledì 29 settembre 2021 15:59<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">marco.cisternino@optimad.it</span></a><span lang="EN-US" class="">><br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" class="">petsc-users@mcs.anl.gov</span></a><span lang="EN-US" class=""><br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [petsc-users] Disconnected domains and Poisson equation</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> The problem actually has a two dimensional null space; constant on each domain but possibly different constants. I think you need to build the MatNullSpace by explicitly constructing two vectors, one with 0 on one domain and constant value on the other and one with 0 on the other domain and constant on the first. <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Separate note: why use FGMRES instead of just GMRES? If the problem is linear and the preconditioner is linear (no GMRES inside the smoother) then you can just use GMRES and it will save a little space/work and be conceptually clearer.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> Barry<o:p class=""></o:p></span></div></div></div><div class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class=""> <o:p class=""></o:p></span></p><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">On Sep 29, 2021, at 8:46 AM, Marco Cisternino <</span><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" class="">marco.cisternino@optimad.it</span></a><span lang="EN-GB" class="">> wrote:<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Good morning,<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I want to solve the Poisson equation on a 3D domain with 2 non-connected sub-domains.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I am using FGMRES+GAMG and I have no problem if the two sub-domains see a Dirichlet boundary condition each.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">On the same domain I would like to solve the Poisson equation imposing periodic boundary condition in one direction and homogenous Neumann boundary conditions in the other two directions. The two sub-domains are symmetric with respect to the separation between them and the operator discretization and the right hand side are symmetric as well. It would be nice to have the same solution in both the sub-domains.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Setting the null space to the constant, the solver converges to a solution having the same gradients in both sub-domains but different values.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Am I doing some wrong with the null space? I’m not setting a block matrix (one block for each sub-domain), should I?<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I tested the null space against the matrix using MatNullSpaceTest and the answer is true. Can I do something more to have a symmetric solution as outcome of the solver?<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thank you in advance for any comments and hints.<o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> <o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Best regards,</span><o:p class=""></o:p></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span><o:p class=""></o:p></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Marco Cisternino</span></div></div></div></div></div></blockquote></div></div></div></div></blockquote></div></div></blockquote></div></div></div></blockquote></div></div></div></blockquote></div><br class=""></body></html>