Jie,
Looks like the direct solver is the best choice except for multigrid. The size
of problem will certainly be limited on a single machine because of the memory
usage. But what if I parallelize my code using distributed-memory? Does dealii
have a parallel version of direct solver?
There is an interface to MUMPS via PETSc, which is a parallel direct solver.
But that's not a solution: if you can apply a direct solver to the top left
block, you may as well apply it to the global system which is not that much
larger. And parallel direct solvers still need far more memory than iterative
solvers.
I'm no expert on the N-S equations, so I don't know what people use as
preconditioners. You'll have to read the literature. Maybe Timo also has
suggestions.
My ultimate problem size will have
less than 10 million dofs. The cluster I have access to has 16G memory on each
node, I can probably use 64 nodes or even more. Will I be able to solve such a
problem using direct solver for system_matrix.block(0,0)?
I suspect that that might work. You'll have ~150,000 unknowns per node,
leaving about 100kB per unknown on each node. That should suffice, though I
have to admit that I don't know how much memory parallel direct solvers need
in 3d. I'd expect a small multiple of 10kB per unknown.
I have no experience in multigrid. Forgive me if I am asking the wrong
question: is algebraic multigrid method a black box comparing to the geometric
one? By black box I mean it requires no additional information other than the
matrix itself hence no additional coding.
That is generally (almost) true if the matrix you apply it to is symmetric and
positive definite. But that's not the case for you.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
For more options, visit https://groups.google.com/d/optout.
