EigenValue Problem

[Nitish Anand]

Hey,

I wish to solve an eigenvalue problem for a rotating disk and to understand more about the implementation I looked into the step-36 example. 

Unfortunately, when I increase the degrees of freedom in the code (changing line 70 to fe(3) or fe(2)) I get the following error.

   Number of active cells:       1024

   Number of degrees of freedom: 9409

   Spurious eigenvalues are all in the interval [86400,170496]

[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------

[0]PETSC ERROR: Zero pivot in LU factorization: http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot

[0]PETSC ERROR: Zero pivot row 15 value 6.77626e-21 tolerance 2.22045e-14

[0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.

[0]PETSC ERROR: Petsc Release Version 3.5.4, May, 23, 2015 

[0]PETSC ERROR: ./step-36 on a x86_64 named tud278242 by nitish Tue Sep 19 14:48:09 2017

[0]PETSC ERROR: Configure options --with-shared-libraries=1 --with-x=0 --with-mpi=1 --download-hypre=1

[0]PETSC ERROR: #1 MatPivotCheck_none() line 622 in /home/nitish/Softwares/petsc-3.5.4/include/petsc-private/matimpl.h

[0]PETSC ERROR: #2 MatPivotCheck() line 641 in /home/nitish/Softwares/petsc-3.5.4/include/petsc-private/matimpl.h

[0]PETSC ERROR: #3 MatLUFactorNumeric_SeqAIJ_Inode() line 1424 in /home/nitish/Softwares/petsc-3.5.4/src/mat/impls/aij/seq/inode.c

[0]PETSC ERROR: #4 MatLUFactorNumeric() line 2893 in /home/nitish/Softwares/petsc-3.5.4/src/mat/interface/matrix.c

[0]PETSC ERROR: #5 PCSetUp_LU() line 152 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/pc/impls/factor/lu/lu.c

[0]PETSC ERROR: #6 PCSetUp() line 902 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/pc/interface/precon.c

[0]PETSC ERROR: #7 KSPSetUp() line 306 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/ksp/interface/itfunc.c

[0]PETSC ERROR: #8 PCSetUp_Redundant() line 170 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/pc/impls/redundant/redundant.c

[0]PETSC ERROR: #9 PCSetUp() line 902 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/pc/interface/precon.c

[0]PETSC ERROR: #10 KSPSetUp() line 306 in /home/nitish/Softwares/petsc-3.5.4/src/ksp/ksp/interface/itfunc.c

[0]PETSC ERROR: #11 STSetUp_Shift() line 132 in /home/nitish/Softwares/slepc-3.5.4/src/sys/classes/st/impls/shift/shift.c

[0]PETSC ERROR: #12 STSetUp() line 301 in /home/nitish/Softwares/slepc-3.5.4/src/sys/classes/st/interface/stsolve.c

[0]PETSC ERROR: #13 EPSSetUp() line 207 in /home/nitish/Softwares/slepc-3.5.4/src/eps/interface/epssetup.c

[0]PETSC ERROR: #14 EPSSolve() line 88 in /home/nitish/Softwares/slepc-3.5.4/src/eps/interface/epssolve.c

ERROR: Uncaught exception in MPI_InitFinalize on proc 0. Skipping MPI_Finalize() to avoid a deadlock.

----------------------------------------------------

Exception on processing: 

--------------------------------------------------------

An error occurred in line <164> of file </home/nitish/Softwares/dealii/source/lac/slepc_solver.cc> in function

    void dealii::SLEPcWrappers::SolverBase::solve(unsigned int, unsigned int*)

The violated condition was: 

    ierr == 0

Additional information: 

        An error with error number 71 occurred while calling a SLEPc function

--------------------------------------------------------

Aborting!

----------------------------------------------------

CMakeFiles/run.dir/build.make:57: recipe for target 'CMakeFiles/run' failed

make[3]: *** [CMakeFiles/run] Error 1

CMakeFiles/Makefile2:264: recipe for target 'CMakeFiles/run.dir/all' failed

make[2]: *** [CMakeFiles/run.dir/all] Error 2

CMakeFiles/Makefile2:271: recipe for target 'CMakeFiles/run.dir/rule' failed

make[1]: *** [CMakeFiles/run.dir/rule] Error 2

Makefile:196: recipe for target 'run' failed

make: *** [run] Error 2

What am I missing here? Thanks for your suggestion.

[Jean-Paul Pelteret]

Dear Nitish,

I’m not familiar with this tutorial and I don’t have much to suggest, but I have one basic question: When increasing the polynomial order of the finite element, do you increase the corresponding quadrature order as well?

Regards,

Jean-Paul

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[Denis Davydov]

Jean-Paul is right. Most likely you don't adjust the quadrature order which breaks LU factorization of the mass matrix, used by default for Generalized Hermitian Eigenvalue Problem. Essentially your mass matrix is not positive definite anymore.

Regards,
Denis

[Nitish Anand]

Thanks, Denis and Jean. Increasing the quadrature order did help me remove this error.