coupled Cahn-Hilliard example doesn't run properly

[guyer]

Although examples/cahnHilliard/mesh2DCoupled.py@fe00adaf9e passes tests, any attempt to increase the size of the mesh causes problems:

• At 100², PySparse needs over 350 MB, likely due to LinearLUSolver.
• Trilinos does not give a sensible solution to the coupled problem, but does fine with the vector equation. They seem to be equivalent.

Although the tests, as written, pass (not that we check very much), we should document that PySparse is not suitable and we need to figure out what's wrong with the coupled treatment.

Imported from trac ticket #582, created by guyer on 03-26-2013 at 13:45, last modified: 09-06-2013 at 10:04

[guyer]

The changes in 8a1f81d 1e56dc5 seem correct, but PySparse still uses a deranged amount of memory and Trilinos doesn't seem to evolve at all (with the default solver)

[guyer]

PETSc (#659) also has problems. Conversely to Trilinos, PETSc can solve the coupled form, but not the vector form. The difference appears to be a bunch of non-zero zeros entered in the matrix for the vector form, e.g.,

vector

0 convergence: KSP_CONVERGED_RTOL 
1 convergence: KSP_CONVERGED_RTOL 
0 iterations: 5 / 1000 
1 iterations: 5 / 1000 
Mat Object: 2 MPI processes
  type: mpiaij
row 0: (0, 9.27582)  (1, -0.)  (2, -0.)  (4, 2.)  (5, -1.)  (6, -1.) 
row 1: (0, -0.)  (1, 9.27582)  (3, -0.)  (4, -1.)  (5, 2.)  (7, -1.) 
row 2: (0, -0.)  (2, 9.27582)  (3, -0.)  (4, -1.)  (6, 2.)  (7, -1.) 
row 3: (1, -0.)  (2, -0.)  (3, 9.27582)  (5, -1.)  (6, -1.)  (7, 2.) 
row 4: (0, -2.)  (1, 1.)  (2, 1.)  (4, 0.0625)  (5, -0.)  (6, -0.) 
row 5: (0, 1.)  (1, -2.)  (3, 1.)  (4, -0.)  (5, 0.0625)  (7, -0.) 
row 6: (0, 1.)  (2, -2.)  (3, 1.)  (4, -0.)  (6, 0.0625)  (7, -0.) 
row 7: (1, 1.)  (2, 1.)  (3, -2.)  (5, -0.)  (6, -0.)  (7, 0.0625) 

coupled

0 convergence: KSP_CONVERGED_RTOL 
1 convergence: KSP_CONVERGED_RTOL 
0 iterations: 4 / 1000 
1 iterations: 4 / 1000 
Mat Object: 2 MPI processes
  type: mpiaij
row 0: (0, 9.27582)  (4, 2.)  (5, -1.)  (6, -1.) 
row 1: (1, 9.27582)  (4, -1.)  (5, 2.)  (7, -1.) 
row 2: (2, 9.27582)  (4, -1.)  (6, 2.)  (7, -1.) 
row 3: (3, 9.27582)  (5, -1.)  (6, -1.)  (7, 2.) 
row 4: (0, -2.)  (1, 1.)  (2, 1.)  (4, 0.0625) 
row 5: (0, 1.)  (1, -2.)  (3, 1.)  (5, 0.0625) 
row 6: (0, 1.)  (2, -2.)  (3, 1.)  (6, 0.0625) 
row 7: (1, 1.)  (2, 1.)  (3, -2.)  (7, 0.0625) 

For 6x6 and below, PETSc gets the same answer, but not if larger.