[petsc-users] SNES Line search: fixing the non zero solution values of dirichlet nodes during line search
Barry Smith
bsmith at petsc.dev
Sat Jun 20 12:00:28 CDT 2020
Ashish,
Based on this " RHS as increment of (Dirichlet_value-solution_value). " I am guessing your inhomogeneous Dirichlet boundary conditions are time dependent, that is u(t) = b(t) for a given b?
If so your problem is really a DAE, not an ODE. You can solve it in several ways:
if b(t) is something you can differentiate then write new boundary conditions as \dot u = \dot b and solve the equations with this new form
otherwise:
solve as a DAE I think just with TSARKIMEX and TS_EQ_DAE_IMPLICIT_INDEX1 with TSSetEquationType and TSARKIMEXSetFullyImplicit but you will need to use TSSetIFunction()/Jaocbian instead of TSRHSFunction/Jacobian
I am cc:ing a couple of others who know much more about ODE integrators than I and may have better approaches.
I don't see any real harm in your in current approach, but there isn't something we can easily add to PETSc "do it for you". I think you will lose some accuracy in your approach because you are just interpolating the know b() at the one new time-steps losing any information about it in the stage values while the approaches above integrate u at the stage locations.
Barry
> On Jun 19, 2020, at 5:15 PM, Ashish Patel <ashish.patel at onscale.com> wrote:
>
> Dear PETSc users,
>
> We use PETSc as part of a finite element method program and we are trying to properly implement Dirichlet boundary conditions for non-linear, transient problems. We find that when we use a line search method it also changes the non-zero solution value of Dirichlet nodes as it steps through the line search iteration. I was wondering if there is a way to freeze some index sets of a vector from changing during the line search operation?
>
> We are using the TS framework to setup the problem and use 'MatZeroRowsColumns' to set the diagonal of the jacobian to 1 for the dirichlet nodes and set the RHS as increment of (Dirichlet_value-solution_value). This works when the line search method is turned off by using '-snes_linesearch_type basic' however using the default 'bt' linesearch, the TS diverges with error shown below. In a separate implementation if we overwrote the dirichlet nodes of the solution vector in TS residual function with the Dirichlet values then the 'bt' line search method converged to the right solution. However we would like to avoid modifying the internal PETSc vector in our implementation.
>
> 0 TS dt 1. time 0.
> 0 SNES Function norm 2.378549386020e+03
> Line search: gnorm after quadratic fit 4.369235425165e+03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.385369069060e+03 lambda=1.0000000000000002e-02
> Line search: Cubically determined step, current gnorm 2.373925008934e+03 lambda=3.8846250444606093e-03
> 1 SNES Function norm 2.373925008934e+03
> Line search: gnorm after quadratic fit 5.006914179995e+03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.420957096780e+03 lambda=1.0000000000000002e-02
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.376034946750e+03 lambda=1.6129422079664700e-03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.374313344729e+03 lambda=4.8465026740690043e-04
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373999473242e+03 lambda=1.5857251532828948e-04
> Line search: Cubically determined step, current gnorm 2.373921668024e+03 lambda=5.8116507162753387e-05
> 2 SNES Function norm 2.373921668024e+03
> Line search: gnorm after quadratic fit 4.771035112853e+03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.410650718394e+03 lambda=1.0000000000000002e-02
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.375104094198e+03 lambda=1.8983783738011522e-03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.374049151562e+03 lambda=7.0688528086485479e-04
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373935090907e+03 lambda=2.9132722794896019e-04
> Line search: Cubically determined step, current gnorm 2.373921032081e+03 lambda=1.2527602265373028e-04
> 3 SNES Function norm 2.373921032081e+03
> Line search: gnorm after quadratic fit 5.117914832660e+03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.422635362094e+03 lambda=1.0000000000000002e-02
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.375923870970e+03 lambda=1.5769887508300913e-03
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.374287081592e+03 lambda=4.8018017100729705e-04
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373999131160e+03 lambda=1.5908966655977892e-04
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373930608274e+03 lambda=5.7603977147935371e-05
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373922022038e+03 lambda=2.3884787050507805e-05
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921396636e+03 lambda=1.0282405393471519e-05
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921173719e+03 lambda=4.3868704034012554e-06
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921091304e+03 lambda=1.8774991151727107e-06
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921057168e+03 lambda=8.0331628193813397e-07
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921042769e+03 lambda=3.4377811174560817e-07
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921036645e+03 lambda=1.4712421886880395e-07
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921034032e+03 lambda=6.2965363212312132e-08
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032916e+03 lambda=2.6947718250469261e-08
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032438e+03 lambda=1.1533043989179318e-08
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032233e+03 lambda=4.9359018284334258e-09
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032146e+03 lambda=2.1124641857409436e-09
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032109e+03 lambda=9.0409137304143975e-10
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032093e+03 lambda=3.8693264359674819e-10
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032086e+03 lambda=1.6559911204766632e-10
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032083e+03 lambda=7.0873187020534353e-11
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=3.0332192901757729e-11
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=1.2981600435512875e-11
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=5.5559212521628090e-12
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=2.3777380405336958e-12
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=1.0176091649134191e-12
> Line search: Cubic step no good, shrinking lambda, current gnorm 2.373921032081e+03 lambda=4.3555419789721080e-13
> Line search: unable to find good step length! After 27 tries
> Line search: fnorm=2.3739210320805191e+03, gnorm=2.3739210320805323e+03, ynorm=8.5698020038772756e+03, minlambda=9.9999999999999998e-13, lambda=4.3555419789721080e-13, initial slope=-5.6355010665542409e+06
> SNES Object: 1 MPI processes
> type: newtonls
> maximum iterations=50, maximum function evaluations=10000
> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08
> total number of linear solver iterations=4
> total number of function evaluations=48
> norm schedule ALWAYS
> SNESLineSearch Object: 1 MPI processes
> type: bt
> interpolation: cubic
> alpha=1.000000e-04
> maxstep=1.000000e+08, minlambda=1.000000e-12
> tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08
> maximum iterations=40
> KSP Object: 1 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: 1 MPI processes
> type: cholesky
> 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: 1 MPI processes
> type: mumps
> rows=38154, cols=38154
> package used to perform factorization: mumps
> total: nonzeros=7080060, allocated nonzeros=7080060
> total number of mallocs used during MatSetValues calls=0
> MUMPS run parameters:
> SYM (matrix type): 2
> PAR (host participation): 1
> ICNTL(1) (output for error): 6
> ICNTL(2) (output of diagnostic msg): 0
> ICNTL(3) (output for global info): 0
> ICNTL(4) (level of printing): 0
> ICNTL(5) (input mat struct): 0
> ICNTL(6) (matrix prescaling): 7
> ICNTL(7) (sequential matrix ordering):7
> ICNTL(8) (scaling strategy): 77
> ICNTL(10) (max num of refinements): 0
> ICNTL(11) (error analysis): 0
> ICNTL(12) (efficiency control): 0
> ICNTL(13) (efficiency control): 0
> ICNTL(14) (percentage of estimated workspace increase): 20
> ICNTL(18) (input mat struct): 0
> ICNTL(19) (Schur complement info): 0
> ICNTL(20) (rhs sparse pattern): 0
> ICNTL(21) (solution struct): 0
> ICNTL(22) (in-core/out-of-core facility): 0
> ICNTL(23) (max size of memory can be allocated locally):0
> ICNTL(24) (detection of null pivot rows): 0
> ICNTL(25) (computation of a null space basis): 0
> ICNTL(26) (Schur options for rhs or solution): 0
> ICNTL(27) (experimental parameter): -32
> ICNTL(28) (use parallel or sequential ordering): 1
> ICNTL(29) (parallel ordering): 0
> ICNTL(30) (user-specified set of entries in inv(A)): 0
> ICNTL(31) (factors is discarded in the solve phase): 0
> ICNTL(33) (compute determinant): 0
> ICNTL(35) (activate BLR based factorization): 0
> ICNTL(36) (choice of BLR factorization variant): 0
> ICNTL(38) (estimated compression rate of LU factors): 333
> CNTL(1) (relative pivoting threshold): 0.01
> CNTL(2) (stopping criterion of refinement): 1.49012e-08
> CNTL(3) (absolute pivoting threshold): 0.
> CNTL(4) (value of static pivoting): -1.
> CNTL(5) (fixation for null pivots): 0.
> CNTL(7) (dropping parameter for BLR): 0.
> RINFO(1) (local estimated flops for the elimination after analysis):
> [0] 2.73979e+09
> RINFO(2) (local estimated flops for the assembly after factorization):
> [0] 1.08826e+07
> RINFO(3) (local estimated flops for the elimination after factorization):
> [0] 2.73979e+09
> INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
> [0] 94
> INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
> [0] 94
> INFO(23) (num of pivots eliminated on this processor after factorization):
> [0] 38154
> RINFOG(1) (global estimated flops for the elimination after analysis): 2.73979e+09
> RINFOG(2) (global estimated flops for the assembly after factorization): 1.08826e+07
> RINFOG(3) (global estimated flops for the elimination after factorization): 2.73979e+09
> (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)
> INFOG(3) (estimated real workspace for factors on all processors after analysis): 8377336
> INFOG(4) (estimated integer workspace for factors on all processors after analysis): 447902
> INFOG(5) (estimated maximum front size in the complete tree): 990
> INFOG(6) (number of nodes in the complete tree): 2730
> INFOG(7) (ordering option effectively use after analysis): 5
> INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
> INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 8377336
> INFOG(10) (total integer space store the matrix factors after factorization): 447902
> INFOG(11) (order of largest frontal matrix after factorization): 990
> INFOG(12) (number of off-diagonal pivots): 10
> INFOG(13) (number of delayed pivots after factorization): 0
> INFOG(14) (number of memory compress after factorization): 0
> INFOG(15) (number of steps of iterative refinement after solution): 0
> INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 94
> INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 94
> INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 94
> INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 94
> INFOG(20) (estimated number of entries in the factors): 7080060
> INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 80
> INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 80
> INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
> INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
> INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
> INFOG(28) (after factorization: number of null pivots encountered): 0
> INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 7080060
> INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 92, 92
> INFOG(32) (after analysis: type of analysis done): 1
> INFOG(33) (value used for ICNTL(8)): 7
> INFOG(34) (exponent of the determinant if determinant is requested): 0
> INFOG(35) (after factorization: number of entries taking into account BLR factor compression - sum over all processors): 7080060
> INFOG(36) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - value on the most memory consuming processor): 0
> INFOG(37) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - sum over all processors): 0
> INFOG(38) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - value on the most memory consuming processor): 0
> INFOG(39) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - sum over all processors): 0
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=38154, cols=38154
> total: nonzeros=973446, allocated nonzeros=973446
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
> [0]PETSC ERROR:
> [0]PETSC ERROR: TSStep has failed due to DIVERGED_NONLINEAR_SOLVE, increase -ts_max_snes_failures or make negative to attempt recovery
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html <https://www.mcs.anl.gov/petsc/documentation/faq.html> for trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.3, Jan, 03, 2020
>
> Thanks,
> Ashish
> Scientific Computing Division
> OnScale
> CA, USA
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