Poor performance with BoomerAMG?

[Barry Smith]

   Trottenberg has a discussion page 178; see the box that begins at  
the bottom of the page and
continues onto the next one). See also the discussion at the bottom of  
page 182 with equations
5.6.14 and 5.6.15,

   I totally disagree with his suggestion of interpolating boundary  
nodes differently from
interior nodes. It makes the code unnecessarily complicated. So long  
as you have the
boundary equations suitably scaled you can simply interpolate  
everywhere identically.

   Barry



On Feb 19, 2008, at 8:21 AM, jens.madsen at risoe.dk wrote:

> 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 at risoe.dk
>
> 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 at mcs.anl.gov [mailto:owner-petsc-users at mcs.anl.gov 
> ] On Behalf Of Barry Smith
> Sent: Saturday, February 16, 2008 6:49 PM
> To: petsc-users at mcs.anl.gov
> 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 at stud.ntnu.no 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 at gmail.com>:
>>>>
>>>>> 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 at stud.ntnu.no 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
>>>>>>
>>>>>>
>>>>
>>>>
>>>>
>>>
>>
>
>