[petsc-users] vector-valued Laplace solver (Navier-Stokes): DIVERGED_INDEFINITE_MAT?

[Nico Schlömer]

Hi all,

I'm trying to solve a discretization of the PDE in weak form

    rho/tau u - mu \Delta u = f

where u is vector-valued (let's say in 2D -- this comes from a
Navier--Stokes problem). Some Dirichlet-boundary conditions come with it,
too.

After translation in weak form,

    rho/tau * inner(u, v) + mu * inner(grad(u), grad(v)) = inner(f, v)

I'm solving this with PETSc's CG and hypre_amg. What I get is

  0 KSP preconditioned resid norm 4.962223194957e+30 true resid norm
2.364095175749e-02 ||r(i)||/||b|| 1.000000000000e+00
  1 KSP preconditioned resid norm 7.089043065444e+19 true resid norm
2.289113027906e-02 ||r(i)||/||b|| 9.682829402926e-01

Without preconditioning, I'm getting

  0 KSP preconditioned resid norm 2.364095175749e-02 true resid norm
2.364095175749e-02 ||r(i)||/||b|| 1.000000000000e+00
  1 KSP preconditioned resid norm 4.415430823612e-02 true resid norm
4.415430823612e-02 ||r(i)||/||b|| 1.867704341562e+00
  2 KSP preconditioned resid norm 1.077641425707e-01 true resid norm
1.077641425707e-01 ||r(i)||/||b|| 4.558367348159e+00

and DIVERGED_INDEFINITE_MAT.

Does anyone else have experience with this sort of problems? Any obvious
mistakes?

--Nico
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