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Re: HYPRE with multiple variables

Hi Barry and Nicolas,

To clarify,

HYPRE_BoomerAMGSetNumFunctions(solver, int num_functions) tells AMG to solve a system of equations with the specified number of functions/unknowns. The default AMG scheme to solve a PDE system is the "unknown" approach. (The coarsening and interpolation are determined by looking at each unknown/function independently - therefore you can imagine that the coarse grids are generally not the same for each variable. This approach generally works well unless you have strong coupling between unknowns.)

HYPRE_BOOMERAMGSetNodal(solver, int nodal ) tells AMG to coarsen such that each variable has the same coarse grid - sometimes this is more "physical" for a particular problem. The value chosen here for nodal determines how strength of connection is determined between the coupled system. I suggest setting nodal = 1, which uses a Frobenius norm. This does NOT tell AMG to use nodal relaxation.

If you want to use nodal relaxation in hypre there are two choices:

(1) If you call HYPRE_BOOMERAMGSetNodal, then you can additionally do nodal relaxation via the schwarz smoother option in hypre. I did not implement this in the Petsc interface, but it could be done easy enough. The following four functions need to be called:

HYPRE_BoomerAMGSetSmoothType(solver, 6);
HYPRE_BoomerAMGSetDomainType(solver, 1);
HYPRE_BoomerAMGSetOverlap(solver, 0);
HYPRE_BoomerAMGSetSmoothNumLevels(solver, num_levels); (Set num_levels to number of levels on which you want nodal smoothing, i.e. 1=just the fine grid, 2= fine grid and the grid below, etc. I find that doing nodal relaxation on just the finest level is generally sufficient.) Note that the interpolation scheme used will be the same as in the unknown approach - so this is what we call a hybrid systems method.

(2) You can do both nodal smoothing and a nodal interpolation scheme. While this is currently implemented in 2.0.0, it is not advertised (i.e., mentioned at all in the user's manual) because it is not yet implemented very efficiently (the fine grid matrix is converted to a block matrix - and both are stored), and we have not found it to be as effective as advertised elsewhere (this is an area of current research for us)..... If you want to try it anyway, let me know and I will provide more info.

Hope this helps,
Allison


Barry Smith wrote: 
  Nicolas,

On Wed, 25 Apr 2007, Nicolas Bathfield wrote:

Dear Barry,

Using MatSetBlockSize(A,5) improved my results greatly. Boomemramg is now
solving the system of equations.

   Good

Still, the equations I solve are coupled, and my discretization scheme is
meant for a non-segregated solver. As a consequence (I believe), boomeramg
still diverges.

How can "Boomeramg be now solving the system of equations" but also diverge? I am so confused.

I would therefore like to use the nodal relaxation in
boomeramg (the hypre command is HYPRE_BOOMERAMGSetNodal) in order to
couple the coarse grid choice for all my variables.

  I can add this this afternoon.

I have to admit I do not understand the difference between HYPRE_BOOMERAMGSetNodal() and hypre_BoomerAMGSetNumFunctions(). Do you?

Barry
How can I achieve this from PETSc?

Best regards,

Nicolas

  From PETSc MPIAIJ matrices you need to set the block size of the matrix
with MatSetBlockSize(A,5) after you have called MatSetType() or
MatCreateMPIAIJ(). Then HYPRE_BoomerAMGSetNumFunctions() is automatically
called by PETSc.

   Barry

The reason this is done this way instead of as
-pc_hypre_boomeramg_block_size <bs> is the idea that hypre will use the
properties of the matrix it is given in building the preconditioner so
the user does not have to pass those properties in seperately directly
to hypre.


On Fri, 13 Apr 2007, Shaman Mahmoudi wrote:

Hi,

int HYPRE_BoomerAMGSetNumFunctions (.....)

sets the size of the system of PDEs.

With best regards, Shaman Mahmoudi

On Apr 13, 2007, at 2:04 PM, Shaman Mahmoudi wrote:

Hi Nicolas,

You are right. hypre has changed a lot since the version I used.

I found this interesting information:

int HYPRE_BOOMERAMGSetNodal(....)

Sets whether to use the nodal systems version. Default is 0.

Then information about smoothers:

One interesting thing there is this,

HYPRE_BoomerAMGSetDomainType(....)

0 - each point is a domain (default)
1 each node is a domain (only of interest in systems AMG)
2 ....

I could not find how you define the nodal displacement ordering. But
it
should be there somewhere.

I read the reference manual for hypre 2.0

With best regards, Shaman Mahmoudi


On Apr 13, 2007, at 1:40 PM, Nicolas Bathfield wrote:

Dear Shaman,

As far as I could understand, there is a BoomerAMG?s systems AMG
version
available. This seems to be exactly what I am looking for, but I
just
don't know how to access it, either through PETSc or directly.

Best regards,

Nicolas

Hi,

You want to exploit the structure of the model?
As far as I know, boomeramg can not treat a set of rows or blocks
as
a molecule,  a so called block-smoother?
ML 2.0 smoothed aggregation does support it.

With best regards, Shaman Mahmoudi

On Apr 13, 2007, at 10:45 AM, Nicolas Bathfield wrote:

Hi,

I am solving the Navier-stokes equations and try to use Hypre as
preconditioner.
Until now, I used PETSc as non-segregated solver and it worked
perfectly.
Things got worse when I decided to use Boomeramg (Hypre).
As I solve a system of PDEs, each cell is represented by 5 rows
in my
matrix (I solve for 5 variables). PETSc handles that without
problem
apparently, but the coarsening scheme of Boomeramg needs more
input in
order to work properly.

Is there an option in PETSc to tell HYPRE that we are dealing
with a
system of PDEs? (something like:  -pc_hypre_boomeramg_...)


Thanks for your help.

Best regards,

Nicolas


--
Nicolas BATHFIELD
Chalmers University of Technology
Shipping and Marine Technology
phone: +46 (0)31 772 1476
fax:   +46 (0)31 772 3699

--
Nicolas BATHFIELD
Chalmers University of Technology
Shipping and Marine Technology
phone: +46 (0)31 772 1476
fax:   +46 (0)31 772 3699