Putting a peculiar multilevel scheme into DMMG?

Jed Brown jed at 59A2.org
Sun Dec 13 08:59:11 CST 2009

I can think of a few ways to implement the following multilevel scheme,
but I'm not sure if it's possible/desirable to have DMMG to manage it.

Finest level       (A)  : DMComposite[DA_2D(dof=1),DA_3D(dof=4+)]
Intermediate level (B)  : DM_2D(dof=3)
Coarsest levels    (C1) : DM_2D(dof=1)
  OR               (C2) : DM_2D(dof=3)

No matrices are assembled on level A, but the smoother involves 1D
solves within columns.  Restriction A->B involves integration and
discarding "slow" quantities.  Assembly is available for Level B and
higher matrices.  There are two coarsening strategies after B, one
involves a fieldsplit where the coarsest grids are only for a scalar
problem, other coarsens B directly.

I think grid sequencing and nonlinear multigrid are not important here
because level B does not contain the long time scales for which
globalization would be challenging.  So this hierarchy is strictly for
preconditioning.  The DMMG interface is rather different from other
components and I recall Barry saying he would like to eventually get rid
of it.  Is there an advantage to using it here?  Unless I'm missing
something, it would require some additions to the API (which I can do if
it is the right thing to do).


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