[petsc-users] How to solve a matrix with zero diagonal entries?

[Song Gao]

Dear Petsc-users,

I modified the code based on KSP ex1f. I'm solving a 2D stream function
vorticity finite element problem. The problem is relatively small, around
2500x2500. I choose to use single processor and LU preconditioner. But the
algorithm set some zeros on the diagonals. By checking the PCLU manual
page, I think I need shift, the code looks like this:

      call KSPGetPC(ksp,preconditioner,ierr)
      call PCSetType(preconditioner,PCLU,ierr)
      call PCFactorSetShiftAmount(preconditioner, 100.0D0,ierr)
      call KSPSetFromOptions(ksp,ierr)
      call KSPSolve(ksp, pet_rhs, pet_sol_update,ierr)

But I still get errors here.

[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 4 value 0 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 3.5.3, Jan, 31, 2015
[0]PETSC ERROR: ./ex1f on a FEM_project named anakin by sgao Mon Apr 20
10:23:58 2015
[0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
--with-fc=gfortran --download-fblaslapack --download-mpich
[0]PETSC ERROR: #1 MatPivotCheck_none() line 622 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/include/petsc-private/matimpl.h
[0]PETSC ERROR: #2 MatPivotCheck() line 641 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/include/petsc-private/matimpl.h
[0]PETSC ERROR: #3 MatLUFactorNumeric_SeqAIJ() line 575 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/mat/impls/aij/seq/aijfact.c
[0]PETSC ERROR: #4 MatLUFactorNumeric() line 2893 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/mat/interface/matrix.c
[0]PETSC ERROR: #5 PCSetUp_LU() line 152 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/ksp/pc/impls/factor/lu/lu.c
[0]PETSC ERROR: #6 PCSetUp() line 902 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/ksp/pc/interface/precon.c
[0]PETSC ERROR: #7 KSPSetUp() line 306 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/ksp/ksp/interface/itfunc.c
[0]PETSC ERROR: #8 KSPSolve() line 418 in
/home/cfd/sgao/public/for_FEM/petsc-3.5.3/src/ksp/ksp/interface/itfunc.c


I tried other run time options, but none of them works. Some gives Zero
pivot errors, some doesn't converge.

./ex1f -pc_factor_shift_type NONZERO -ksp_monitor_true_residual -ksp_max_it
10

./ex1f -pc_factor_shift_type NONZERO -pc_factor_shift_amount 1
 -ksp_monitor_true_residual -ksp_max_it 10

./ex1f -pc_factor_shift_type POSITIVE_DEFINITE -pc_factor_shift_amount 1
 -ksp_monitor_true_residual -ksp_max_it 10

./ex1f  -pc_factor_nonzeros_along_diagonal -ksp_monitor_true_residual
-ksp_max_it 10

The matrix on a small grid is attached. Thanks
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