[petsc-users] Solving eigenproblems in the form of Stokes equations

[Julian Andrej]

Hi,

i'm trying to solve a generalized eigenvalue problem which is the
stokes equations discretized by finite elements (with fenics) and
producing a banded matrix (reordered structure) of the well known
block form

[N    Q]
[QT  0]

The domain is the unit square with dirichlet boundary condition
evaluating to zero at all boundary nodes.

A is the block matrix in banded reordered structure and M is the mass matrix.

I'm using slepc4py for the eigenvalue calculation.

E = SLEPc.EPS().create()
E.setOperators(A, M)
E.setDimensions(NEV, PETSc.DECIDE)
E.setFromOptions()

I always get the error
[0] Zero pivot row 1 value 0 tolerance 2.22045e-14

I cannot find a combination which solves the eigenvalues for this problem.

The system itself solves fine with a KSP solver object from PETSc
using tfmqr with the icc PC.

I can assemble the matrix with a penalty term for the pressure and
calculate the eigenvalues with a direct solver, but i try to avoid
that.