[petsc-users] strange convergence
Hoang Giang Bui
hgbk2008 at gmail.com
Wed May 3 02:29:13 CDT 2017
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?
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
> > <https://drive.google.com/file/d/0Bw8Hmu0-YGQXc2hKQ1BhQ1I4OEU/view?usp=
> drive_web>
> >
> >
> > 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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