<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><pre style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); position: static; z-index: auto; ">Matt, </pre><pre style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); position: static; z-index: auto; ">Thank you for your help.</pre><pre style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); position: static; z-index: auto; "><blockquote type="cite">On Mon, Feb 20, 2012 at 2:05 PM, Max Rudolph <<a href="https://lists.mcs.anl.gov/mailman/listinfo/petsc-users">rudolph at berkeley.edu</a>> wrote:
><i> Hi Dave,
</i>><i> Thanks for your help.
</i>><i>
</i>><i> Max
</i>><i>
</i>><i> Hey Max,
</i>><i>
</i>><i> Without knowing anything about the specific application related to
</i>><i> your Stokes problem, or information about the mesh you are using, I
</i>><i> have a couple of questions and suggestions which might help.
</i>><i>
</i>><i>
</i>><i> The test case that I am working with is isoviscous convection, benchmark
</i>><i> case 1a from Blankenbach 1989.
</i>><i>
</i>><i> 1) If A, is your stokes operator A = ( K,B ; B^T, 0 ), what is your
</i>><i> precondition operator?
</i>><i> Specifically, what is in the (2,2) slot in the precondioner? - i.e.
</i>><i> what matrix are you you applying -stokes_fieldsplit_1_pc_type jacobi
</i>><i> -stokes_fieldsplit_1_ksp_type preonly to?
</i>><i> Is it the identity as in the SpeedUp notes?
</i>><i>
</i>><i>
</i>><i> I think that this is the problem. The (2,2) slot in the LHS matrix is all
</i>><i> zero (pressure does not appear in the continuity equation), so I think that
</i>><i> the preconditioner is meaningless. I am still confused as to why this
</i>><i> choice of preconditioner was suggested in the tutorial, and what is a
</i>><i> better choice of preconditioner for this block? Should I be using one of
</i>><i> the Schur complement methods instead of the additive or multiplicative
</i>><i> field split?
</i>><i>
</i>
Its not suggested, it is demonstrated. Its the first logical choice, since
Jacobi gives the identity for a 0 block (see
<a href="http://www.jstor.org/pss/2158202">http://www.jstor.org/pss/2158202</a>). Its
not meaningless. All the better preconditioners involve either a Schur
complement (also shown in the tutorial), or an auxiliary operator which is
more
difficult to setup and thus not shown.<br></blockquote><br></pre><pre style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); position: static; z-index: auto; ">Thank you for clarifying this.</pre><pre style="color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); position: static; z-index: auto; "><blockquote type="cite">
><i> 2) This choice
</i>><i> -stokes_fieldsplit_0_pc_type ml -stokes_fieldsplit_0_ksp_type preonly
</i>><i> may simply not be a very effective and degrade the performance of the
</i>><i> outer solver.
</i>><i> I'd make the solver for the operator in the (1,1) slot much stronger,
</i>><i> for example
</i>><i> -stokes_fieldsplit_0_ksp_type gmres
</i>><i> -stokes_fieldsplit_0_ksp_rtol 1.0e-4
</i>><i> -stokes_fieldsplit_0_mg_levels_ksp_type gmres
</i>><i> -stokes_fieldsplit_0_mg_levels_pc_type bjacobi
</i>><i> -stokes_fieldsplit_0_mg_levels_ksp_max_it 4
</i>><i>
</i>><i> Add a monitor on this solver (-stokes_fieldsplit_0_ksp_XXX) to see how
</i>><i> ML is doing.
</i>><i>
</i>><i> 3) Using -stokes_pc_fieldsplit_type MULTIPLICATIVE should reduce the
</i>><i> number of outer iterations by a factor of two, but it will use more
</i>><i> memory.
</i>><i>
</i>><i> 4) You should use a flexible Krylov method on the outer most solve
</i>><i> (-stokes_ksp_XXX) as the preconditioner is varying between each outer
</i>><i> iteration. Use -stokes_ksp_type fgmres or -stokes_ksp_type gcr
</i>><i>
</i>><i>
</i>><i> Thanks for pointing this out. I made that change.
</i>><i>
</i>><i> 5) Depending on how the physical problem is scaled
</i>><i> (non-dimensionalised), the size of the residuals associated with the
</i>><i> momentum and continuity equation make be quite different. You are
</i>><i> currently use the entire residual from (u,p) to determine when to stop
</i>><i> iterating. You might want to consider writing a monitor which examines
</i>><i> the these residuals independently.
</i>><i>
</i>><i>
</i>><i> I think that I have scaled the problem correctly. I (slowly) obtain a
</i>><i> sufficiently accurate solution using as options only:
</i>><i> -stokes_ksp_atol 1e-5 -stokes_ksp_rtol 1e-5
</i>><i> -stokes_ksp_monitor_true_residual -stokes_ksp_norm_type UNPRECONDITIONED
</i>><i>
</i>
How do you know the problem is scaled correctly? Have you looked at norms
of the residuals for the two systems</blockquote><blockquote type="cite"> Thanks,
Matt
><i> Cheers,
</i>><i> Dave</i></blockquote></pre><div><br></div>Yes, here are the norms computed for the P, X, and Y components, following the last residual that ksp_monitor_true_residual returned:<br><br>383 KSP unpreconditioned resid norm 1.121628211019e-03 true resid norm 1.121628224178e-03 ||r(i)||/||b|| 9.626787321554e-10<br>P, X, Y residual norms 5.340336e-02, 4.463404e-02, 2.509621e-02<br><br><br><br></body></html>