[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: Poor performance with BoomerAMG?


All multigrid solvers depend on proper scaling of the variables. For example
for a Laplacian operator the matrix entries are

        \integral \grad \phi_i dot \grad \phi_j

now in 2d \grad \phi is O(1/h) and the volume is O(h^2) so the terms
in the matrix are O(1). In 3d \grad \phi is still O(1/h) but the volume is O(h^3)
meaning the matrix entries are O(h). Now say you impose a Dirichlet boundary
conditions by just saying u_k = g_k. In 2d this is ok but in 3d you need to
use h*u_k = h*g_k otherwise when you restrict to the coarser grid the
resulting matrix entries for the boundary are "out of whack" with the matrix
entries for the interior of the domain.

Actually most preconditioners and Krylov methods behavior does depend
on the row scaling; multigrid is just particularly sensitive.

   Barry


On Feb 15, 2008, at 5:36 PM, Andrew T Barker wrote:



Be careful how you handle boundary conditions; you need to make sure
they have the same scaling as the other equations.

Could you clarify what you mean? Is boomerAMG sensitive to scaling of matrix rows in a way that other solvers/preconditioners are not?

Andrew


On Feb 15, 2008, at 8:36 AM, knutert@xxxxxxxxxxxx wrote:

Hi Ben,

Thank you for answering. With gmres and boomeramg I get a run time of
2s, so that is much better. However, if I increase the grid size to
513x513, I get a run time of one minute. With richardson, it fails
to converge.
LU gives 6 seconds, CG and ICC gives 7s, and the DMMG solver 3s for
the 513x513 problem.

When using the DMMG framework, I just used the default solvers.
I use the Galerkin process to generate the coarse matrices for
the multigrid cycle.

Best,
Knut

Siterer Ben Tay <zonexo@xxxxxxxxx>:

Hi Knut,

I'm currently using boomeramg to solve my poisson eqn too. I'm
using it
on my structured C-grid. I found it to be faster than LU,
especially as
the grid size increases. However I use it as a preconditioner with
GMRES as the solver. Have you tried this option? Although it's
faster,
the speed increase is usually less than double. It seems to be
worse if
there is a lot of stretching in the grid.

Btw, your mention using the DMMG framework and it takes less than a
sec. What solver or preconditioner did you use? It's 4 times faster
than GMRES...

thanks!

knutert@xxxxxxxxxxxx wrote: 
Hello,

I am trying to use the hypre multigrid solver to solve a Poisson
equation.
However, on a test case with grid size 257x257 it takes 40
seconds  to converge
on one processor when I run with
./run -ksp_type richardson -pc_type hypre -pc_type_hypre boomeramg

Using the DMMG framework, the same problem takes less than a second,
and the default gmres solver uses only four seconds.

Am I somehow using the solver the wrong way, or is this
performance  expected?

Regards
Knut Erik Teigen