Hi Barry
Two questions.
1) What do you mean with "volume" and "wrong scaling"? Could
translate this to some other terms? I have a book by Ulrich
Trottenberg "Multigrid" and the book by Saad, but could not find
similar.
2) Do you know of any summerschools in scientific computing,
focusing on Krylov methods, multigrids and preconditioning(all
parallel)?
Kind Regards
Jens Madsen
Ph.d.-studerende
Phone direct +45 4677 4560
Mobile
jens.madsen@xxxxxxxx
Optics and Plasma Research Department
Risø National Laboratory
Technical University of Denmark - DTU
Building 128, P.O. Box 49
DK-4000 Roskilde, Denmark
Tel +45 4677 4500
Fax +45 4677 4565
www.risoe.dk
From 1 January 2007, Risø National Laboratory, the Danish Institute
for Food and Veterinary Research,
the Danish Institute for Fisheries Research, the Danish National
Space Center and
the Danish Transport Research Institute have been merged with
the Technical University of Denmark (DTU) with DTU as the continuing
unit.
-----Original Message-----
From: owner-petsc-users@xxxxxxxxxxx [mailto:owner-petsc-users@xxxxxxxxxxx
] On Behalf Of Barry Smith
Sent: Saturday, February 16, 2008 6:49 PM
To: petsc-users@xxxxxxxxxxx
Subject: 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