[firedrake] Multi-grid preconditioning

[Justin Chang]

Hi Lawrence (or anyone),

So I attempted multigrid on the following LSFEM problem:

#========================
#  Discretization
#========================
mesh = UnitCubeMesh(seed, seed, seed)
V = VectorFunctionSpace(mesh,"CG",2)
Q = FunctionSpace(mesh,"CG", 1)
W = V * Q
v, p = TrialFunctions(W)
w, q = TestFunctions(W)

#========================
#  Forcing function
#========================
f = Function(Q)
f.interpolate(Expression("12*pi*pi*sin(pi*x[0]*2)*sin(pi*x[1]*2)*sin(2*pi*x[2])"))

#========================
#  Weak form
#========================
a = dot(v+grad(p),w+grad(q))*dx + div(v)*div(w)*dx
L = f*div(w)*dx


...


with these solver options:


-ksp_type cg

-pc_type fieldsplit

-pc_fieldsplit_type multiplicative

-pc_fieldsplit_0_ksp_type preonly

-pc_fieldsplit_0_pc_type hypre

-pc_fieldsplit_1_ksp_type preonly

-pc_fieldsplit_1_pc_type hypre


attached is the full code.

Run as:

python Darcy_LS.py <seed> 1

where <seed> is number of cells in each direction

Though the solution is correct, the code converges extremely slow, even if
VectorFunctionSpace is CG1. The number of iterations grow with size.

I have tried other options like schur, additive, etc, but it seems this
option is the "best" w.r.t. wall-clock time. Do you know if there's a
better preconditioner for this problem? Or should I defer this question to
someplace else?

Thanks,
Justin


On Tue, Aug 4, 2015 at 4:32 PM, Justin Chang <jychang48 at gmail.com> wrote:

> Okay I will give this a try, thanks!
>
> On Wed, Jul 29, 2015 at 2:13 PM, Lawrence Mitchell <
> lawrence.mitchell at imperial.ac.uk> wrote:
>
>>
>>
>> > On 29 Jul 2015, at 17:26, Justin Chang <jychang48 at gmail.com> wrote:
>> >
>> > Is there support for Multi-grid preconditioning? I think I saw
>> somewhere where this was not supported yet. Because applying -pc_type gamg
>> for my mixed forms returns me errors.
>>
>> If you want to apply AMG to your mixed form, you'll need to assemble a
>> monolithic matrix. Pass nest=False when either assembling the operator or
>> building your solver.
>>
>> However, this may not work well, you might want to do gamg on one of the
>> blocks, using fieldsplit preconditioners: all the normal PETSc options work.
>>
>> Lawrence
>> _______________________________________________
>> firedrake mailing list
>> firedrake at imperial.ac.uk
>> https://mailman.ic.ac.uk/mailman/listinfo/firedrake
>>
>
>
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