mixed Helmholtz failure about firedrake

[wence-]

I think the problem is that your system is getting really badly conditioned and gmres is losing too much information in the restart. If I run with:

solver_parameters={'ksp_gmres_restart': 200, 'ksp_monitor_singular_value': True}

I get convergence of the largest problem:

L_inf norm: 0.131777047356
L2 norm: 0.131777047355
L_inf norm: 0.146869663844
L2 norm: 0.059711026174
L_inf norm: 0.0389459143339
L2 norm: 0.01596968206
L_inf norm: 0.0107924786456
L2 norm: 0.00426911884399

But PETSc estimates the condition number of the last problem as 6e5, and it takes 5100 iterations to converge (the system has 21000 dofs).

In conclusion, can you build a better PC by using schur complements?

[wence-]

Answer, yes:

   solve(a == L, out, solver_parameters={'pc_type': 'fieldsplit',
                                          'pc_fieldsplit_type': 'schur',
                                          'ksp_type': 'cg',
                                          'pc_fieldsplit_schur_fact_type': 'FULL',
                                          'fieldsplit_0_ksp_type': 'cg',
                                          'fieldsplit_1_ksp_type': 'cg',
                                          'ksp_monitor': True})

    Residual norms for firedrake_snes_0_ solve.
    0 KSP Residual norm 9.416491472343e+00 
    1 KSP Residual norm 1.853245163915e-11 
L_inf norm: 0.131777047356
L2 norm: 0.131777047355
    Residual norms for firedrake_snes_1_ solve.
    0 KSP Residual norm 6.507015022039e+00 
    1 KSP Residual norm 2.674064589955e-12 
L_inf norm: 0.146868545809
L2 norm: 0.0597100588258
    Residual norms for firedrake_snes_2_ solve.
    0 KSP Residual norm 1.592744048817e+01 
    1 KSP Residual norm 3.561132153579e-05 
    2 KSP Residual norm 1.700162704754e-10 
L_inf norm: 0.0389818965915
L2 norm: 0.0159811969722
    Residual norms for firedrake_snes_3_ solve.
    0 KSP Residual norm 4.509605854437e+01 
    1 KSP Residual norm 5.140400988667e-05 
    2 KSP Residual norm 3.452288755060e-10 
L_inf norm: 0.0098520605559
L2 norm: 0.0040541386656

In about 3 seconds.

[wence-]

Is this appropriately addressed?

[dorugeber]

i think i'm happy with it now.

[kynan]

What does "happy" mean? Do we get the right answer or not?

[wence-]

This test is in master and passing, hence closing.