# [petsc-users] strange convergence

Dave May dave.mayhem23 at gmail.com
Wed May 3 02:45:04 CDT 2017

On Wed, 3 May 2017 at 09:29, Hoang Giang Bui <hgbk2008 at gmail.com> wrote:

> Dear Jed
>
> 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. Do you or anyone already have
> experience using discrete Lagrange multiplier space with Petsc?
>

Yes - this is similar to solving incompressible Stokes in which the
pressure is a Lagrange multiplier enforcing the div(v)=0 constraint.

Robust preconditioners for this problem are constructed using PCFIELDSPLIT.

Thanks,
Dave

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