[petsc-users] KSP_DIVERGED_INDEFINITE_PC message even with PCFactorSetShiftType

[Evan Um]

Dear PETSC Users,

I try to solve a diffusion problem in the time domain. Its system matrix is
theoretically SPD. I use KSPCG solver. Direct MUMPS solver generates a
preconditioner. Thus, within 1-2 iterations, a solution is expected to
converge. Such convergence is observed in most test problems. However, in
some test problems, I get non-convergence with a message:
KSP_DIVERGED_INDEFINITE_PC. This problem is alleviated when I use
PCFactorSetShiftType(pc_fetd_dt,MAT_SHIFT_POSITIVE_DEFINITE). However, the
indefiniteness error message occurs later during time-stepping. I am aware
of PETSC function PCFactorSetShiftAmount. However, before I try this, I
couldn't find the information about a default shift amount when I use
PCFactorSetShiftType(pc_fetd_dt,MAT_SHIFT_POSITIVE_DEFINITE). How can I
find the default shift amount?

More generally, how can I stably solve SPD problems that are close to
indefiniteness using KSP options? To get the reference solution, I was able
to solve the same problem above using SuiteSparse (serial) but its solution
time was not practical.

In advance, thanks for your advice.

Regards,
Evan

Sample Code:

KSPCreate(PETSC_COMM_WORLD, &ksp_fetd_dt);

KSPSetOperators(ksp_fetd_dt, A_dt, A_dt);

KSPSetType (ksp_fetd_dt, KSPPREONLY);

KSPGetPC(ksp_fetd_dt, &pc_fetd_dt);

MatSetOption(A_dt, MAT_SPD, PETSC_TRUE);

PCSetType(pc_fetd_dt, PCCHOLESKY);

PCFactorSetMatSolverPackage(pc_fetd_dt, MATSOLVERMUMPS);

PCFactorSetUpMatSolverPackage(pc_fetd_dt);

PCFactorGetMatrix(pc_fetd_dt, &F_dt);

KSPSetType(ksp_fetd_dt, KSPCG);

PCFactorSetShiftType(pc_fetd_dt,MAT_SHIFT_POSITIVE_DEFINITE);
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