<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Wed, May 3, 2017 at 2:29 AM, Hoang Giang Bui <span dir="ltr"><<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Dear Jed<div><br></div><div>If I understood you correctly you suggest to avoid penalty by using the Lagrange multiplier for the mortar constraint? In this case it leads to the use of discrete Lagrange multiplier space.</div></div></blockquote><div><br></div><div>Sorry for being ignorant here, but why is the space "discrete"? It looks like you should have a continuum formulation</div><div>of the mortar as well. Maybe I do not understand something fundamental. From this (<a href="https://en.wikipedia.org/wiki/Mortar_methods">https://en.wikipedia.org/wiki/Mortar_methods</a>)</div><div>short description, it seems that mortars begin from a continuum formulation, but are then reduced to the discrete level. This is no</div><div>problem if done consistently, as for instance in the FETI method where efficient preconditioners exist.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Do you or anyone already have experience using discrete Lagrange multiplier space with Petsc?</div><div class="gmail_extra"><br></div><div class="gmail_extra">There is also similar question on stackexchange</div><div class="gmail_extra"><a href="https://scicomp.stackexchange.com/questions/25113/preconditioners-and-discrete-lagrange-multipliers" target="_blank">https://scicomp.stackexchange.<wbr>com/questions/25113/<wbr>preconditioners-and-discrete-<wbr>lagrange-multipliers</a><br></div><div class="gmail_extra"><br clear="all"><div><div class="gmail-m_6948412756754771881gmail_signature"><div dir="ltr">Giang</div></div></div>
<br><div class="gmail_quote">On Sat, Apr 29, 2017 at 3:34 PM, Jed Brown <span dir="ltr"><<a href="mailto:jed@jedbrown.org" target="_blank">jed@jedbrown.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><span class="gmail-m_6948412756754771881gmail-">Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>> writes:<br>
<br>
> Hi Barry<br>
><br>
> The first block is from a standard solid mechanics discretization based on<br>
> balance of momentum equation. There is some material involved but in<br>
> principal it's well-posed elasticity equation with positive definite<br>
> tangent operator. The "gluing business" uses the mortar method to keep the<br>
> continuity of displacement. Instead of using Lagrange multiplier to treat<br>
> the constraint I used penalty method to penalize the energy. The<br>
> discretization form of mortar is quite simple<br>
><br>
> \int_{\Gamma_1} { rho * (\delta u_1 - \delta u_2) * (u_1 - u_2) dA }<br>
><br>
> rho is penalty parameter. In the simulation I initially set it low (~E) to<br>
> preserve the conditioning of the system.<br>
<br>
</span>There are two things that can go wrong here with AMG:<br>
<br>
* The penalty term can mess up the strength of connection heuristics<br>
such that you get poor choice of C-points (classical AMG like<br>
BoomerAMG) or poor choice of aggregates (smoothed aggregation).<br>
<br>
* The penalty term can prevent Jacobi smoothing from being effective; in<br>
this case, it can lead to poor coarse basis functions (higher energy<br>
than they should be) and poor smoothing in an MG cycle. You can fix<br>
the poor smoothing in the MG cycle by using a stronger smoother, like<br>
ASM with some overlap.<br>
<br>
I'm generally not a fan of penalty methods due to the irritating<br>
tradeoffs and often poor solver performance.<br>
<span class="gmail-m_6948412756754771881gmail-"><br>
> In the figure below, the colorful blocks are u_1 and the base is u_2. Both<br>
> u_1 and u_2 use isoparametric quadratic approximation.<br>
><br>
> <br>
</span>> Snapshot.png<br>
> <<a href="https://drive.google.com/file/d/0Bw8Hmu0-YGQXc2hKQ1BhQ1I4OEU/view?usp=drive_web" rel="noreferrer" target="_blank">https://drive.google.com/file<wbr>/d/0Bw8Hmu0-YGQXc2hKQ1BhQ1I4OE<wbr>U/view?usp=drive_web</a>><br>
<div class="gmail-m_6948412756754771881gmail-HOEnZb"><div class="gmail-m_6948412756754771881gmail-h5">> <br>
><br>
> Giang<br>
><br>
> On Fri, Apr 28, 2017 at 6:21 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>> wrote:<br>
><br>
>><br>
>> Ok, so boomerAMG algebraic multigrid is not good for the first block.<br>
>> You mentioned the first block has two things glued together? AMG is<br>
>> fantastic for certain problems but doesn't work for everything.<br>
>><br>
>> Tell us more about the first block, what PDE it comes from, what<br>
>> discretization, and what the "gluing business" is and maybe we'll have<br>
>> suggestions for how to precondition it.<br>
>><br>
>> Barry<br>
>><br>
>> > On Apr 28, 2017, at 3:56 AM, Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>> wrote:<br>
>> ><br>
>> > It's in fact quite good<br>
>> ><br>
>> > Residual norms for fieldsplit_u_ solve.<br>
>> > 0 KSP Residual norm 4.014715925568e+00<br>
>> > 1 KSP Residual norm 2.160497019264e-10<br>
>> > Residual norms for fieldsplit_wp_ solve.<br>
>> > 0 KSP Residual norm 0.000000000000e+00<br>
>> > 0 KSP preconditioned resid norm 4.014715925568e+00 true resid norm<br>
>> 9.006493082896e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > Residual norms for fieldsplit_u_ solve.<br>
>> > 0 KSP Residual norm 9.999999999416e-01<br>
>> > 1 KSP Residual norm 7.118380416383e-11<br>
>> > Residual norms for fieldsplit_wp_ solve.<br>
>> > 0 KSP Residual norm 0.000000000000e+00<br>
>> > 1 KSP preconditioned resid norm 1.701150951035e-10 true resid norm<br>
>> 5.494262251846e-04 ||r(i)||/||b|| 6.100334726599e-11<br>
>> > Linear solve converged due to CONVERGED_ATOL iterations 1<br>
>> ><br>
>> > Giang<br>
>> ><br>
>> > On Thu, Apr 27, 2017 at 5:25 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>> wrote:<br>
>> ><br>
>> > Run again using LU on both blocks to see what happens.<br>
>> ><br>
>> ><br>
>> > > On Apr 27, 2017, at 2:14 AM, Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>><br>
>> wrote:<br>
>> > ><br>
>> > > I have changed the way to tie the nonconforming mesh. It seems the<br>
>> matrix now is better<br>
>> > ><br>
>> > > with -pc_type lu the output is<br>
>> > > 0 KSP preconditioned resid norm 3.308678584240e-01 true resid norm<br>
>> 9.006493082896e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > 1 KSP preconditioned resid norm 2.004313395301e-12 true resid norm<br>
>> 2.549872332830e-05 ||r(i)||/||b|| 2.831148938173e-12<br>
>> > > Linear solve converged due to CONVERGED_ATOL iterations 1<br>
>> > ><br>
>> > ><br>
>> > > with -pc_type fieldsplit -fieldsplit_u_pc_type hypre<br>
>> -fieldsplit_wp_pc_type lu the convergence is slow<br>
>> > > 0 KSP preconditioned resid norm 1.116302362553e-01 true resid norm<br>
>> 9.006493083520e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > 1 KSP preconditioned resid norm 2.582134825666e-02 true resid norm<br>
>> 9.268347719866e+06 ||r(i)||/||b|| 1.029073984060e+00<br>
>> > > ...<br>
>> > > 824 KSP preconditioned resid norm 1.018542387738e-09 true resid norm<br>
>> 2.906608839310e+02 ||r(i)||/||b|| 3.227237074804e-05<br>
>> > > 825 KSP preconditioned resid norm 9.743727947637e-10 true resid norm<br>
>> 2.820369993061e+02 ||r(i)||/||b|| 3.131485215062e-05<br>
>> > > Linear solve converged due to CONVERGED_ATOL iterations 825<br>
>> > ><br>
>> > > checking with additional -fieldsplit_u_ksp_type richardson<br>
>> -fieldsplit_u_ksp_monitor -fieldsplit_u_ksp_max_it 1<br>
>> -fieldsplit_wp_ksp_type richardson -fieldsplit_wp_ksp_monitor<br>
>> -fieldsplit_wp_ksp_max_it 1 gives<br>
>> > ><br>
>> > > 0 KSP preconditioned resid norm 1.116302362553e-01 true resid norm<br>
>> 9.006493083520e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > Residual norms for fieldsplit_u_ solve.<br>
>> > > 0 KSP Residual norm 5.803507549280e-01<br>
>> > > 1 KSP Residual norm 2.069538175950e-01<br>
>> > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > 1 KSP preconditioned resid norm 2.582134825666e-02 true resid norm<br>
>> 9.268347719866e+06 ||r(i)||/||b|| 1.029073984060e+00<br>
>> > > Residual norms for fieldsplit_u_ solve.<br>
>> > > 0 KSP Residual norm 7.831796195225e-01<br>
>> > > 1 KSP Residual norm 1.734608520110e-01<br>
>> > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > ....<br>
>> > > 823 KSP preconditioned resid norm 1.065070135605e-09 true resid norm<br>
>> 3.081881356833e+02 ||r(i)||/||b|| 3.421843916665e-05<br>
>> > > Residual norms for fieldsplit_u_ solve.<br>
>> > > 0 KSP Residual norm 6.113806394327e-01<br>
>> > > 1 KSP Residual norm 1.535465290944e-01<br>
>> > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > 824 KSP preconditioned resid norm 1.018542387746e-09 true resid norm<br>
>> 2.906608839353e+02 ||r(i)||/||b|| 3.227237074851e-05<br>
>> > > Residual norms for fieldsplit_u_ solve.<br>
>> > > 0 KSP Residual norm 6.123437055586e-01<br>
>> > > 1 KSP Residual norm 1.524661826133e-01<br>
>> > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > 825 KSP preconditioned resid norm 9.743727947718e-10 true resid norm<br>
>> 2.820369990571e+02 ||r(i)||/||b|| 3.131485212298e-05<br>
>> > > Linear solve converged due to CONVERGED_ATOL iterations 825<br>
>> > ><br>
>> > ><br>
>> > > The residual for wp block is zero since in this first step the rhs is<br>
>> zero. As can see in the output, the multigrid does not perform well to<br>
>> reduce the residual in the sub-solve. Is my observation right? what can be<br>
>> done to improve this?<br>
>> > ><br>
>> > ><br>
>> > > Giang<br>
>> > ><br>
>> > > On Tue, Apr 25, 2017 at 12:17 AM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
>> wrote:<br>
>> > ><br>
>> > > This can happen in the matrix is singular or nearly singular or if<br>
>> the factorization generates small pivots, which can occur for even<br>
>> nonsingular problems if the matrix is poorly scaled or just plain nasty.<br>
>> > ><br>
>> > ><br>
>> > > > On Apr 24, 2017, at 5:10 PM, Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>><br>
>> wrote:<br>
>> > > ><br>
>> > > > It took a while, here I send you the output<br>
>> > > ><br>
>> > > > 0 KSP preconditioned resid norm 3.129073545457e+05 true resid norm<br>
>> 9.015150492169e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > > 1 KSP preconditioned resid norm 7.442444222843e-01 true resid norm<br>
>> 1.003356247696e+02 ||r(i)||/||b|| 1.112966720375e-05<br>
>> > > > 2 KSP preconditioned resid norm 3.267453132529e-07 true resid norm<br>
>> 3.216722968300e+01 ||r(i)||/||b|| 3.568130084011e-06<br>
>> > > > 3 KSP preconditioned resid norm 1.155046883816e-11 true resid norm<br>
>> 3.234460376820e+01 ||r(i)||/||b|| 3.587805194854e-06<br>
>> > > > Linear solve converged due to CONVERGED_ATOL iterations 3<br>
>> > > > KSP Object: 4 MPI processes<br>
>> > > > type: gmres<br>
>> > > > GMRES: restart=1000, using Modified Gram-Schmidt<br>
>> Orthogonalization<br>
>> > > > GMRES: happy breakdown tolerance 1e-30<br>
>> > > > maximum iterations=1000, initial guess is zero<br>
>> > > > tolerances: relative=1e-20, absolute=1e-09, divergence=10000<br>
>> > > > left preconditioning<br>
>> > > > using PRECONDITIONED norm type for convergence test<br>
>> > > > PC Object: 4 MPI processes<br>
>> > > > type: lu<br>
>> > > > LU: out-of-place factorization<br>
>> > > > tolerance for zero pivot 2.22045e-14<br>
>> > > > matrix ordering: natural<br>
>> > > > factor fill ratio given 0, needed 0<br>
>> > > > Factored matrix follows:<br>
>> > > > Mat Object: 4 MPI processes<br>
>> > > > type: mpiaij<br>
>> > > > rows=973051, cols=973051<br>
>> > > > package used to perform factorization: pastix<br>
>> > > > Error : 3.24786e-14<br>
>> > > > total: nonzeros=0, allocated nonzeros=0<br>
>> > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > PaStiX run parameters:<br>
>> > > > Matrix type : Unsymmetric<br>
>> > > > Level of printing (0,1,2): 0<br>
>> > > > Number of refinements iterations : 3<br>
>> > > > Error : 3.24786e-14<br>
>> > > > linear system matrix = precond matrix:<br>
>> > > > Mat Object: 4 MPI processes<br>
>> > > > type: mpiaij<br>
>> > > > rows=973051, cols=973051<br>
>> > > > Error : 3.24786e-14<br>
>> > > > total: nonzeros=9.90037e+07, allocated nonzeros=9.90037e+07<br>
>> > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > using I-node (on process 0) routines: found 78749 nodes, limit<br>
>> used is 5<br>
>> > > > Error : 3.24786e-14<br>
>> > > ><br>
>> > > > It doesn't do as you said. Something is not right here. I will look<br>
>> in depth.<br>
>> > > ><br>
>> > > > Giang<br>
>> > > ><br>
>> > > > On Mon, Apr 24, 2017 at 8:21 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
>> wrote:<br>
>> > > ><br>
>> > > > > On Apr 24, 2017, at 12:47 PM, Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>><br>
>> wrote:<br>
>> > > > ><br>
>> > > > > Good catch. I get this for the very first step, maybe at that time<br>
>> the rhs_w is zero.<br>
>> > > ><br>
>> > > > With the multiplicative composition the right hand side of the<br>
>> second solve is the initial right hand side of the second solve minus<br>
>> A_10*x where x is the solution to the first sub solve and A_10 is the lower<br>
>> left block of the outer matrix. So unless both the initial right hand side<br>
>> has a zero for the second block and A_10 is identically zero the right hand<br>
>> side for the second sub solve should not be zero. Is A_10 == 0?<br>
>> > > ><br>
>> > > ><br>
>> > > > > In the later step, it shows 2 step convergence<br>
>> > > > ><br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 3.165886479830e+04<br>
>> > > > > 1 KSP Residual norm 2.905922877684e-01<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 2.397669419027e-01<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 0 KSP preconditioned resid norm 3.165886479920e+04 true resid<br>
>> norm 7.963616922323e+05 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 9.999891813771e-01<br>
>> > > > > 1 KSP Residual norm 1.512000395579e-05<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 8.192702188243e-06<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 1 KSP preconditioned resid norm 5.252183822848e-02 true resid<br>
>> norm 7.135927677844e+04 ||r(i)||/||b|| 8.960661653427e-02<br>
>> > > ><br>
>> > > > The outer residual norms are still wonky, the preconditioned<br>
>> residual norm goes from 3.165886479920e+04 to 5.252183822848e-02 which is a<br>
>> huge drop but the 7.963616922323e+05 drops very much less<br>
>> 7.135927677844e+04. This is not normal.<br>
>> > > ><br>
>> > > > What if you just use -pc_type lu for the entire system (no<br>
>> fieldsplit), does the true residual drop to almost zero in the first<br>
>> iteration (as it should?). Send the output.<br>
>> > > ><br>
>> > > ><br>
>> > > ><br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 6.946213936597e-01<br>
>> > > > > 1 KSP Residual norm 1.195514007343e-05<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 1.025694497535e+00<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 2 KSP preconditioned resid norm 8.785709535405e-03 true resid<br>
>> norm 1.419341799277e+04 ||r(i)||/||b|| 1.782282866091e-02<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 7.255149996405e-01<br>
>> > > > > 1 KSP Residual norm 6.583512434218e-06<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 1.015229700337e+00<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 3 KSP preconditioned resid norm 7.110407712709e-04 true resid<br>
>> norm 5.284940654154e+02 ||r(i)||/||b|| 6.636357205153e-04<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 3.512243341400e-01<br>
>> > > > > 1 KSP Residual norm 2.032490351200e-06<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 1.282327290982e+00<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 4 KSP preconditioned resid norm 3.482036620521e-05 true resid<br>
>> norm 4.291231924307e+01 ||r(i)||/||b|| 5.388546393133e-05<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 3.423609338053e-01<br>
>> > > > > 1 KSP Residual norm 4.213703301972e-07<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 1.157384757538e+00<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 5 KSP preconditioned resid norm 1.203470314534e-06 true resid<br>
>> norm 4.544956156267e+00 ||r(i)||/||b|| 5.707150658550e-06<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 3.838596289995e-01<br>
>> > > > > 1 KSP Residual norm 9.927864176103e-08<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 1.066298905618e+00<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 6 KSP preconditioned resid norm 3.331619244266e-08 true resid<br>
>> norm 2.821511729024e+00 ||r(i)||/||b|| 3.543002829675e-06<br>
>> > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > 0 KSP Residual norm 4.624964188094e-01<br>
>> > > > > 1 KSP Residual norm 6.418229775372e-08<br>
>> > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > 0 KSP Residual norm 9.800784311614e-01<br>
>> > > > > 1 KSP Residual norm 0.000000000000e+00<br>
>> > > > > 7 KSP preconditioned resid norm 8.788046233297e-10 true resid<br>
>> norm 2.849209671705e+00 ||r(i)||/||b|| 3.577783436215e-06<br>
>> > > > > Linear solve converged due to CONVERGED_ATOL iterations 7<br>
>> > > > ><br>
>> > > > > The outer operator is an explicit matrix.<br>
>> > > > ><br>
>> > > > > Giang<br>
>> > > > ><br>
>> > > > > On Mon, Apr 24, 2017 at 7:32 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
>> wrote:<br>
>> > > > ><br>
>> > > > > > On Apr 24, 2017, at 3:16 AM, Hoang Giang Bui <<a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>><br>
>> wrote:<br>
>> > > > > ><br>
>> > > > > > Thanks Barry, trying with -fieldsplit_u_type lu gives better<br>
>> convergence. I still used 4 procs though, probably with 1 proc it should<br>
>> also be the same.<br>
>> > > > > ><br>
>> > > > > > The u block used a Nitsche-type operator to connect two<br>
>> non-matching domains. I don't think it will leave some rigid body motion<br>
>> leads to not sufficient constraints. Maybe you have other idea?<br>
>> > > > > ><br>
>> > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > 0 KSP Residual norm 3.129067184300e+05<br>
>> > > > > > 1 KSP Residual norm 5.906261468196e-01<br>
>> > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > ><br>
>> > > > > ^^^^ something is wrong here. The sub solve should not be<br>
>> starting with a 0 residual (this means the right hand side for this sub<br>
>> solve is zero which it should not be).<br>
>> > > > ><br>
>> > > > > > FieldSplit with MULTIPLICATIVE composition: total splits = 2<br>
>> > > > ><br>
>> > > > ><br>
>> > > > > How are you providing the outer operator? As an explicit matrix<br>
>> or with some shell matrix?<br>
>> > > > ><br>
>> > > > ><br>
>> > > > ><br>
>> > > > > > 0 KSP preconditioned resid norm 3.129067184300e+05 true resid<br>
>> norm 9.015150492169e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > 0 KSP Residual norm 9.999955993437e-01<br>
>> > > > > > 1 KSP Residual norm 4.019774691831e-06<br>
>> > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > > > 1 KSP preconditioned resid norm 5.003913641475e-01 true resid<br>
>> norm 4.692996324114e+01 ||r(i)||/||b|| 5.205677185522e-06<br>
>> > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > 0 KSP Residual norm 1.000012180204e+00<br>
>> > > > > > 1 KSP Residual norm 1.017367950422e-05<br>
>> > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > > > 2 KSP preconditioned resid norm 2.330910333756e-07 true resid<br>
>> norm 3.474855463983e+01 ||r(i)||/||b|| 3.854461960453e-06<br>
>> > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > 0 KSP Residual norm 1.000004200085e+00<br>
>> > > > > > 1 KSP Residual norm 6.231613102458e-06<br>
>> > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > > > 3 KSP preconditioned resid norm 8.671259838389e-11 true resid<br>
>> norm 3.545103468011e+01 ||r(i)||/||b|| 3.932384125024e-06<br>
>> > > > > > Linear solve converged due to CONVERGED_ATOL iterations 3<br>
>> > > > > > KSP Object: 4 MPI processes<br>
>> > > > > > type: gmres<br>
>> > > > > > GMRES: restart=1000, using Modified Gram-Schmidt<br>
>> Orthogonalization<br>
>> > > > > > GMRES: happy breakdown tolerance 1e-30<br>
>> > > > > > maximum iterations=1000, initial guess is zero<br>
>> > > > > > tolerances: relative=1e-20, absolute=1e-09, divergence=10000<br>
>> > > > > > left preconditioning<br>
>> > > > > > using PRECONDITIONED norm type for convergence test<br>
>> > > > > > PC Object: 4 MPI processes<br>
>> > > > > > type: fieldsplit<br>
>> > > > > > FieldSplit with MULTIPLICATIVE composition: total splits = 2<br>
>> > > > > > Solver info for each split is in the following KSP objects:<br>
>> > > > > > Split number 0 Defined by IS<br>
>> > > > > > KSP Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > type: richardson<br>
>> > > > > > Richardson: damping factor=1<br>
>> > > > > > maximum iterations=1, initial guess is zero<br>
>> > > > > > tolerances: relative=1e-05, absolute=1e-50,<br>
>> divergence=10000<br>
>> > > > > > left preconditioning<br>
>> > > > > > using PRECONDITIONED norm type for convergence test<br>
>> > > > > > PC Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > type: lu<br>
>> > > > > > LU: out-of-place factorization<br>
>> > > > > > tolerance for zero pivot 2.22045e-14<br>
>> > > > > > matrix ordering: natural<br>
>> > > > > > factor fill ratio given 0, needed 0<br>
>> > > > > > Factored matrix follows:<br>
>> > > > > > Mat Object: 4 MPI processes<br>
>> > > > > > type: mpiaij<br>
>> > > > > > rows=938910, cols=938910<br>
>> > > > > > package used to perform factorization: pastix<br>
>> > > > > > total: nonzeros=0, allocated nonzeros=0<br>
>> > > > > > Error : 3.36878e-14<br>
>> > > > > > total number of mallocs used during MatSetValues calls<br>
>> =0<br>
>> > > > > > PaStiX run parameters:<br>
>> > > > > > Matrix type : Unsymmetric<br>
>> > > > > > Level of printing (0,1,2): 0<br>
>> > > > > > Number of refinements iterations : 3<br>
>> > > > > > Error : 3.36878e-14<br>
>> > > > > > linear system matrix = precond matrix:<br>
>> > > > > > Mat Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > type: mpiaij<br>
>> > > > > > rows=938910, cols=938910, bs=3<br>
>> > > > > > Error : 3.36878e-14<br>
>> > > > > > Error : 3.36878e-14<br>
>> > > > > > total: nonzeros=8.60906e+07, allocated<br>
>> nonzeros=8.60906e+07<br>
>> > > > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > > > using I-node (on process 0) routines: found 78749<br>
>> nodes, limit used is 5<br>
>> > > > > > Split number 1 Defined by IS<br>
>> > > > > > KSP Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > type: richardson<br>
>> > > > > > Richardson: damping factor=1<br>
>> > > > > > maximum iterations=1, initial guess is zero<br>
>> > > > > > tolerances: relative=1e-05, absolute=1e-50,<br>
>> divergence=10000<br>
>> > > > > > left preconditioning<br>
>> > > > > > using PRECONDITIONED norm type for convergence test<br>
>> > > > > > PC Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > type: lu<br>
>> > > > > > LU: out-of-place factorization<br>
>> > > > > > tolerance for zero pivot 2.22045e-14<br>
>> > > > > > matrix ordering: natural<br>
>> > > > > > factor fill ratio given 0, needed 0<br>
>> > > > > > Factored matrix follows:<br>
>> > > > > > Mat Object: 4 MPI processes<br>
>> > > > > > type: mpiaij<br>
>> > > > > > rows=34141, cols=34141<br>
>> > > > > > package used to perform factorization: pastix<br>
>> > > > > > Error : -nan<br>
>> > > > > > Error : -nan<br>
>> > > > > > Error : -nan<br>
>> > > > > > total: nonzeros=0, allocated nonzeros=0<br>
>> > > > > > total number of mallocs used during MatSetValues<br>
>> calls =0<br>
>> > > > > > PaStiX run parameters:<br>
>> > > > > > Matrix type : Symmetric<br>
>> > > > > > Level of printing (0,1,2): 0<br>
>> > > > > > Number of refinements iterations : 0<br>
>> > > > > > Error : -nan<br>
>> > > > > > linear system matrix = precond matrix:<br>
>> > > > > > Mat Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > type: mpiaij<br>
>> > > > > > rows=34141, cols=34141<br>
>> > > > > > total: nonzeros=485655, allocated nonzeros=485655<br>
>> > > > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > > > not using I-node (on process 0) routines<br>
>> > > > > > linear system matrix = precond matrix:<br>
>> > > > > > Mat Object: 4 MPI processes<br>
>> > > > > > type: mpiaij<br>
>> > > > > > rows=973051, cols=973051<br>
>> > > > > > total: nonzeros=9.90037e+07, allocated nonzeros=9.90037e+07<br>
>> > > > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > > > using I-node (on process 0) routines: found 78749 nodes,<br>
>> limit used is 5<br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > > Giang<br>
>> > > > > ><br>
>> > > > > > On Sun, Apr 23, 2017 at 10:19 PM, Barry Smith <<br>
>> <a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>> wrote:<br>
>> > > > > ><br>
>> > > > > > > On Apr 23, 2017, at 2:42 PM, Hoang Giang Bui <<br>
>> <a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>> wrote:<br>
>> > > > > > ><br>
>> > > > > > > Dear Matt/Barry<br>
>> > > > > > ><br>
>> > > > > > > With your options, it results in<br>
>> > > > > > ><br>
>> > > > > > > 0 KSP preconditioned resid norm 1.106709687386e+31 true<br>
>> resid norm 9.015150491938e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > > 0 KSP Residual norm 2.407308987203e+36<br>
>> > > > > > > 1 KSP Residual norm 5.797185652683e+72<br>
>> > > > > ><br>
>> > > > > > It looks like Matt is right, hypre is seemly producing useless<br>
>> garbage.<br>
>> > > > > ><br>
>> > > > > > First how do things run on one process. If you have similar<br>
>> problems then debug on one process (debugging any kind of problem is always<br>
>> far easy on one process).<br>
>> > > > > ><br>
>> > > > > > First run with -fieldsplit_u_type lu (instead of using hypre) to<br>
>> see if that works or also produces something bad.<br>
>> > > > > ><br>
>> > > > > > What is the operator and the boundary conditions for u? It could<br>
>> be singular.<br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > > > > ...<br>
>> > > > > > > 999 KSP preconditioned resid norm 2.920157329174e+12 true<br>
>> resid norm 9.015683504616e+06 ||r(i)||/||b|| 1.000059124102e+00<br>
>> > > > > > > Residual norms for fieldsplit_u_ solve.<br>
>> > > > > > > 0 KSP Residual norm 1.533726746719e+36<br>
>> > > > > > > 1 KSP Residual norm 3.692757392261e+72<br>
>> > > > > > > Residual norms for fieldsplit_wp_ solve.<br>
>> > > > > > > 0 KSP Residual norm 0.000000000000e+00<br>
>> > > > > > ><br>
>> > > > > > > Do you suggest that the pastix solver for the "wp" block<br>
>> encounters small pivot? In addition, seem like the "u" block is also<br>
>> singular.<br>
>> > > > > > ><br>
>> > > > > > > Giang<br>
>> > > > > > ><br>
>> > > > > > > On Sun, Apr 23, 2017 at 7:39 PM, Barry Smith <<br>
>> <a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>> wrote:<br>
>> > > > > > ><br>
>> > > > > > > Huge preconditioned norms but normal unpreconditioned norms<br>
>> almost always come from a very small pivot in an LU or ILU factorization.<br>
>> > > > > > ><br>
>> > > > > > > The first thing to do is monitor the two sub solves. Run<br>
>> with the additional options -fieldsplit_u_ksp_type richardson<br>
>> -fieldsplit_u_ksp_monitor -fieldsplit_u_ksp_max_it 1<br>
>> -fieldsplit_wp_ksp_type richardson -fieldsplit_wp_ksp_monitor<br>
>> -fieldsplit_wp_ksp_max_it 1<br>
>> > > > > > ><br>
>> > > > > > > > On Apr 23, 2017, at 12:22 PM, Hoang Giang Bui <<br>
>> <a href="mailto:hgbk2008@gmail.com" target="_blank">hgbk2008@gmail.com</a>> wrote:<br>
>> > > > > > > ><br>
>> > > > > > > > Hello<br>
>> > > > > > > ><br>
>> > > > > > > > I encountered a strange convergence behavior that I have<br>
>> trouble to understand<br>
>> > > > > > > ><br>
>> > > > > > > > KSPSetFromOptions completed<br>
>> > > > > > > > 0 KSP preconditioned resid norm 1.106709687386e+31 true<br>
>> resid norm 9.015150491938e+06 ||r(i)||/||b|| 1.000000000000e+00<br>
>> > > > > > > > 1 KSP preconditioned resid norm 2.933141742664e+29 true<br>
>> resid norm 9.015152282123e+06 ||r(i)||/||b|| 1.000000198575e+00<br>
>> > > > > > > > 2 KSP preconditioned resid norm 9.686409637174e+16 true<br>
>> resid norm 9.015354521944e+06 ||r(i)||/||b|| 1.000022631902e+00<br>
>> > > > > > > > 3 KSP preconditioned resid norm 4.219243615809e+15 true<br>
>> resid norm 9.017157702420e+06 ||r(i)||/||b|| 1.000222648583e+00<br>
>> > > > > > > > .....<br>
>> > > > > > > > 999 KSP preconditioned resid norm 3.043754298076e+12 true<br>
>> resid norm 9.015425041089e+06 ||r(i)||/||b|| 1.000030454195e+00<br>
>> > > > > > > > 1000 KSP preconditioned resid norm 3.043000287819e+12 true<br>
>> resid norm 9.015424313455e+06 ||r(i)||/||b|| 1.000030373483e+00<br>
>> > > > > > > > Linear solve did not converge due to DIVERGED_ITS iterations<br>
>> 1000<br>
>> > > > > > > > KSP Object: 4 MPI processes<br>
>> > > > > > > > type: gmres<br>
>> > > > > > > > GMRES: restart=1000, using Modified Gram-Schmidt<br>
>> Orthogonalization<br>
>> > > > > > > > GMRES: happy breakdown tolerance 1e-30<br>
>> > > > > > > > maximum iterations=1000, initial guess is zero<br>
>> > > > > > > > tolerances: relative=1e-20, absolute=1e-09,<br>
>> divergence=10000<br>
>> > > > > > > > left preconditioning<br>
>> > > > > > > > using PRECONDITIONED norm type for convergence test<br>
>> > > > > > > > PC Object: 4 MPI processes<br>
>> > > > > > > > type: fieldsplit<br>
>> > > > > > > > FieldSplit with MULTIPLICATIVE composition: total splits<br>
>> = 2<br>
>> > > > > > > > Solver info for each split is in the following KSP<br>
>> objects:<br>
>> > > > > > > > Split number 0 Defined by IS<br>
>> > > > > > > > KSP Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > > > type: preonly<br>
>> > > > > > > > maximum iterations=10000, initial guess is zero<br>
>> > > > > > > > tolerances: relative=1e-05, absolute=1e-50,<br>
>> divergence=10000<br>
>> > > > > > > > left preconditioning<br>
>> > > > > > > > using NONE norm type for convergence test<br>
>> > > > > > > > PC Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > > > type: hypre<br>
>> > > > > > > > HYPRE BoomerAMG preconditioning<br>
>> > > > > > > > HYPRE BoomerAMG: Cycle type V<br>
>> > > > > > > > HYPRE BoomerAMG: Maximum number of levels 25<br>
>> > > > > > > > HYPRE BoomerAMG: Maximum number of iterations PER<br>
>> hypre call 1<br>
>> > > > > > > > HYPRE BoomerAMG: Convergence tolerance PER hypre<br>
>> call 0<br>
>> > > > > > > > HYPRE BoomerAMG: Threshold for strong coupling 0.6<br>
>> > > > > > > > HYPRE BoomerAMG: Interpolation truncation factor 0<br>
>> > > > > > > > HYPRE BoomerAMG: Interpolation: max elements per row<br>
>> 0<br>
>> > > > > > > > HYPRE BoomerAMG: Number of levels of aggressive<br>
>> coarsening 0<br>
>> > > > > > > > HYPRE BoomerAMG: Number of paths for aggressive<br>
>> coarsening 1<br>
>> > > > > > > > HYPRE BoomerAMG: Maximum row sums 0.9<br>
>> > > > > > > > HYPRE BoomerAMG: Sweeps down 1<br>
>> > > > > > > > HYPRE BoomerAMG: Sweeps up 1<br>
>> > > > > > > > HYPRE BoomerAMG: Sweeps on coarse 1<br>
>> > > > > > > > HYPRE BoomerAMG: Relax down<br>
>> symmetric-SOR/Jacobi<br>
>> > > > > > > > HYPRE BoomerAMG: Relax up<br>
>> symmetric-SOR/Jacobi<br>
>> > > > > > > > HYPRE BoomerAMG: Relax on coarse<br>
>> Gaussian-elimination<br>
>> > > > > > > > HYPRE BoomerAMG: Relax weight (all) 1<br>
>> > > > > > > > HYPRE BoomerAMG: Outer relax weight (all) 1<br>
>> > > > > > > > HYPRE BoomerAMG: Using CF-relaxation<br>
>> > > > > > > > HYPRE BoomerAMG: Measure type local<br>
>> > > > > > > > HYPRE BoomerAMG: Coarsen type PMIS<br>
>> > > > > > > > HYPRE BoomerAMG: Interpolation type classical<br>
>> > > > > > > > linear system matrix = precond matrix:<br>
>> > > > > > > > Mat Object: (fieldsplit_u_) 4 MPI processes<br>
>> > > > > > > > type: mpiaij<br>
>> > > > > > > > rows=938910, cols=938910, bs=3<br>
>> > > > > > > > total: nonzeros=8.60906e+07, allocated<br>
>> nonzeros=8.60906e+07<br>
>> > > > > > > > total number of mallocs used during MatSetValues<br>
>> calls =0<br>
>> > > > > > > > using I-node (on process 0) routines: found 78749<br>
>> nodes, limit used is 5<br>
>> > > > > > > > Split number 1 Defined by IS<br>
>> > > > > > > > KSP Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > > > type: preonly<br>
>> > > > > > > > maximum iterations=10000, initial guess is zero<br>
>> > > > > > > > tolerances: relative=1e-05, absolute=1e-50,<br>
>> divergence=10000<br>
>> > > > > > > > left preconditioning<br>
>> > > > > > > > using NONE norm type for convergence test<br>
>> > > > > > > > PC Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > > > type: lu<br>
>> > > > > > > > LU: out-of-place factorization<br>
>> > > > > > > > tolerance for zero pivot 2.22045e-14<br>
>> > > > > > > > matrix ordering: natural<br>
>> > > > > > > > factor fill ratio given 0, needed 0<br>
>> > > > > > > > Factored matrix follows:<br>
>> > > > > > > > Mat Object: 4 MPI processes<br>
>> > > > > > > > type: mpiaij<br>
>> > > > > > > > rows=34141, cols=34141<br>
>> > > > > > > > package used to perform factorization: pastix<br>
>> > > > > > > > Error : -nan<br>
>> > > > > > > > Error : -nan<br>
>> > > > > > > > total: nonzeros=0, allocated nonzeros=0<br>
>> > > > > > > > Error : -nan<br>
>> > > > > > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > > > > > PaStiX run parameters:<br>
>> > > > > > > > Matrix type :<br>
>> Symmetric<br>
>> > > > > > > > Level of printing (0,1,2): 0<br>
>> > > > > > > > Number of refinements iterations : 0<br>
>> > > > > > > > Error : -nan<br>
>> > > > > > > > linear system matrix = precond matrix:<br>
>> > > > > > > > Mat Object: (fieldsplit_wp_) 4 MPI processes<br>
>> > > > > > > > type: mpiaij<br>
>> > > > > > > > rows=34141, cols=34141<br>
>> > > > > > > > total: nonzeros=485655, allocated nonzeros=485655<br>
>> > > > > > > > total number of mallocs used during MatSetValues<br>
>> calls =0<br>
>> > > > > > > > not using I-node (on process 0) routines<br>
>> > > > > > > > linear system matrix = precond matrix:<br>
>> > > > > > > > Mat Object: 4 MPI processes<br>
>> > > > > > > > type: mpiaij<br>
>> > > > > > > > rows=973051, cols=973051<br>
>> > > > > > > > total: nonzeros=9.90037e+07, allocated<br>
>> nonzeros=9.90037e+07<br>
>> > > > > > > > total number of mallocs used during MatSetValues calls =0<br>
>> > > > > > > > using I-node (on process 0) routines: found 78749<br>
>> nodes, limit used is 5<br>
>> > > > > > > ><br>
>> > > > > > > > The pattern of convergence gives a hint that this system is<br>
>> somehow bad/singular. But I don't know why the preconditioned error goes up<br>
>> too high. Anyone has an idea?<br>
>> > > > > > > ><br>
>> > > > > > > > Best regards<br>
>> > > > > > > > Giang Bui<br>
>> > > > > > > ><br>
>> > > > > > ><br>
>> > > > > > ><br>
>> > > > > ><br>
>> > > > > ><br>
>> > > > ><br>
>> > > > ><br>
>> > > ><br>
>> > > ><br>
>> > ><br>
>> > ><br>
>> ><br>
>> ><br>
>><br>
>><br>
</div></div></blockquote></div><br></div></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
</div></div>