MatMerge_SeqsToMPI

[Barry Smith]

On May 23, 2008, at 11:20 AM, Waad Subber wrote:

> Thank you for the useful comments. For sure I will consider them.  
> I've just starting my research by writing a DDM substructuring code  
> which scales for now up-to 60 CPUs using petsc KSP solver for the  
> interface problem and Lapack direct factorization for the interior  
> problem. I split the domain using METIS library and assign each  
> subdomain to one process then solve the global Schur complement  
> using parallel preconditioned iterative solver. As an initial  
> attempt, I solved a 2D elasticity problem (about 100,000 DOFs)  
> within seconds using this algorithm. I notice Lapack solver for the  
> interior problem takes a lot of time compare to the iterative solver  
> for the interface, so now I am replacing the direct factorization  
> with petsc KSP solver.

    In my experience you will want to use a KSP direct solve, for  
example just -ksp_type preonly -pc_type lu; using an iterative solver  
in such Schur complement is
always way to slow.

   Barry

>
>
> I would like very much to have a look at your implementation, and I  
> think that will be very useful to me.
>
> Thanks
>
> Waad
>
> Lisandro Dalcin <dalcinl at gmail.com> wrote: On 5/20/08, Waad Subber  
> wrote:
> > 1) How do you actually get the local Schur complements. You
> > explicitelly compute its entries, or do you compute it after  
> computing
> > the inverse (or LU factors) of a 'local' matrix?
> >
> > I construct the local Schur complement matrices after getting the  
> inversion
> > of A_II matrix for each subdomain.
>
> Fine,
>
> > 2) Your R_i matrix is actually a matrix? In that case, it is a  
> trivial
> > restrinction operation with ones and zeros? Or R_i is actually a
> > VecScatter?
> >
> > R_i is the restriction matrix maps the global boundary nodes to  
> the local
> > boundary nodes and its entries is zero and one I store it as spare  
> matrix,
> > so only I need to store the nonzero entries which one entry per a  
> row
>
> I believe a VecScatter will perform much better for this task.
>
>
> > And finally: are you trying to apply a Krylov method over the global
> > Schur complement? In such a case, are you going to implement a
> > preconditioner for it?
> >
> > Yes, that what I am trying to do
>
> Well, please let me make some comments. I've spent many days and month
> optimizing Schur complement iterations, and I ended giving up. I was
> never able to get it perform better than ASM preconditioner (iff
> appropriatelly used, ie. solving local problems with LU, and
> implementing subdomain subpartitioning the smart way, not the way
> currently implemented in PETSc, were subpartitioning is done by chunks
> of continuous rows).
>
> If you are doing research on this, I would love to know your
> conclusion when you get your work done. If you are doing all this just
> with the hope of getting better running times, well, remember my above
> comments but also remember that I do not consider myself a smart guy
> ;-)
>
> As I said before, I worked hard for implementing general Schur
> complement iteration. All this code is avalable in the SVN repository
> of petsc4py (PETSc for Python), but it could be easily stripped out
> for use in any PETSc-based code in C/C++. This implementation requires
> the use of a MATIS matrix type (there is also a separate
> implementation for MATMPIAIJ maatrices), I've implemented subdomain
> subpartitioning (using a simple recursive graph splitting procedure
> reusing matrix reordering routines built-in in PETSc, could be done
> better with METIS); when the A_ii problems are large, their LU
> factorization can be a real bootleneck. I've even implemented a
> global preconditioner operation for the interface problem, based on
> iterating over a 'strip' of nodes around the interface; it improves
> convergence and is usefull for ill-conditioned systems, but the costs
> are increased.
>
> If you ever want to take a look at my implemention for try to use it,
> or perhaps take ideas for your own implementation, let me know.
>
>
>
>
>
> > > Now having the Schur complement matrix for each subdomain, I  
> need to solve
> > > the interface problem
> > (Sum[R_i^T*S_i*R_i])u=Sum[R_i^T*g_i],
> > > .. i=1.. to No. of process (subdomains) in parallel.
> > >
> > > For the global vector I construct one MPI vector and use  
> VecGetArray ()
> > for
> > > each of the sequential vector then use VecSetValues () to add  
> the values
> > > into the global MPI vector. That works fine.
> > >
> > > However for the global schur complement matix I try the same  
> idea by
> > > creating one parallel MPIAIJ matrix and using MatGetArray( ) and
> > > MatSetValues () in order to add the values to the global matrix.
> > > MatGetArray( ) gives me only the values without indices, so I  
> don't know
> > how
> > > to add these valuse to the global MPI matrix.
> > >
> > > Thanks agin
> > >
> > > Waad
> > >
> > > Barry Smith wrote:
> > >
> > > On May 20, 2008, at 3:16 PM, Waad Subber wrote:
> > >
> > > > Thank you Matt,
> > > >
> > > > Any suggestion to solve the problem I am trying to tackle. I  
> want to
> > > > solve a linear system:
> > > >
> > > > Sum(A_i) u= Sum(f_i) , i=1.... to No. of CPUs.
> > > >
> > > > Where A_i is a sparse sequential matrix and f_i is a sequential
> > > > vector. Each CPU has one matrix and one vector of the same  
> size. Now
> > > > I want to sum up and solve the system in parallel.
> > >
> > > Does each A_i have nonzero entries (mostly) associated with one
> > > part of the matrix? Or does each process have values
> > > scattered all around the matrix?
> > >
> > > In the former case you should simply create one parallel MPIAIJ
> > > matrix and call MatSetValues() to put the values
> > > into it. We don't have any kind of support for the later case,  
> perhaps
> > > if you describe how the matrix entries come about someone
> > > would have suggestions on how to proceed.
> > >
> > > Barry
> > >
> > > >
> > > >
> > > > Thanks again
> > > >
> > > > Waad
> > > >
> > > > Matthew Knepley wrote: On Tue, May 20, 2008 at
> > > > 2:12 PM, Waad Subber wrote:
> > > > > Hi,
> > > > >
> > > > > I am trying to construct a sparse parallel matrix (MPIAIJ) by
> > > > adding up
> > > > > sparse sequential matrices (SeqAIJ) from each CPU. I am using
> > > > >
> > > > > MatMerge_SeqsToMPI(MPI_Comm comm,Mat seqmat,PetscInt  
> m,PetscInt
> > > > n,MatReuse
> > > > > scall,Mat *mpimat)
> > > > >
> > > > > to do that. However, when I compile the code I get the  
> following
> > > > >
> > > > > undefined reference to `matmerge_seqstompi_'
> > > > > collect2: ld returned 1 exit status
> > > > > make: *** [all] Error 1
> > > > >
> > > > > Am I using this function correctly ?
> > > >
> > > > These have no Fortran bindings right now.
> > > >
> > > > Matt
> > > >
> > > > > Thanks
> > > > >
> > > > > Waad
> > > > >
> > > >
> > > >
> > > >
> > > > --
> > > > What most experimenters take for granted before they begin their
> > > > experiments is infinitely more interesting than any results to  
> which
> > > > their experiments lead.
> > > > -- Norbert Wiener
> > > >
> > > >
> > > >
> > >
> > >
> > >
> > >
> > >
> >
> >
> > --
> > Lisandro Dalcín
> > ---------------
> > Centro Internacional de Métodos Computacionales en Ingeniería  
> (CIMEC)
> > Instituto de Desarrollo Tecnológico para la Industria Química  
> (INTEC)
> > Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> > PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> > Tel/Fax: +54-(0)342-451.1594
> >
> >
> >
> >
> >
>
>
> -- 
> Lisandro Dalcín
> ---------------
> Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
> Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
> Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> Tel/Fax: +54-(0)342-451.1594
>
>
>