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.<br><br>I would like very much to have a look at your implementation, and I think that will be very useful to me.<br><br>Thanks <br><br>Waad<br><br><b><i>Lisandro Dalcin <dalcinl@gmail.com></i></b> wrote:<blockquote class="replbq"
style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"> On 5/20/08, Waad Subber <w_subber@yahoo.com> wrote:<br>> 1) How do you actually get the local Schur complements. You<br>> explicitelly compute its entries, or do you compute it after computing<br>> the inverse (or LU factors) of a 'local' matrix?<br>><br>> I construct the local Schur complement matrices after getting the inversion<br>> of A_II matrix for each subdomain.<br><br>Fine,<br><br>> 2) Your R_i matrix is actually a matrix? In that case, it is a trivial<br>> restrinction operation with ones and zeros? Or R_i is actually a<br>> VecScatter?<br>><br>> R_i is the restriction matrix maps the global boundary nodes to the local<br>> boundary nodes and its entries is zero and one I store it as spare matrix,<br>> so only I need to store the nonzero entries which one entry per a row<br><br>I believe a VecScatter will perform much better for this
task.<br><br><br>> And finally: are you trying to apply a Krylov method over the global<br>> Schur complement? In such a case, are you going to implement a<br>> preconditioner for it?<br>><br>> Yes, that what I am trying to do<br><br>Well, please let me make some comments. I've spent many days and month<br>optimizing Schur complement iterations, and I ended giving up. I was<br>never able to get it perform better than ASM preconditioner (iff<br>appropriatelly used, ie. solving local problems with LU, and<br>implementing subdomain subpartitioning the smart way, not the way<br>currently implemented in PETSc, were subpartitioning is done by chunks<br>of continuous rows).<br><br>If you are doing research on this, I would love to know your<br>conclusion when you get your work done. If you are doing all this just<br>with the hope of getting better running times, well, remember my above<br>comments but also remember that I do not consider myself a smart
guy<br>;-)<br><br>As I said before, I worked hard for implementing general Schur<br>complement iteration. All this code is avalable in the SVN repository<br>of petsc4py (PETSc for Python), but it could be easily stripped out<br>for use in any PETSc-based code in C/C++. This implementation requires<br>the use of a MATIS matrix type (there is also a separate<br>implementation for MATMPIAIJ maatrices), I've implemented subdomain<br>subpartitioning (using a simple recursive graph splitting procedure<br>reusing matrix reordering routines built-in in PETSc, could be done<br>better with METIS); when the A_ii problems are large, their LU<br>factorization can be a real bootleneck. I've even implemented a<br>global preconditioner operation for the interface problem, based on<br>iterating over a 'strip' of nodes around the interface; it improves<br>convergence and is usefull for ill-conditioned systems, but the costs<br>are increased.<br><br>If you ever want to take a look at my
implemention for try to use it,<br>or perhaps take ideas for your own implementation, let me know.<br><br><br><br><br><br>> > Now having the Schur complement matrix for each subdomain, I need to solve<br>> > the interface problem<br>> (Sum[R_i^T*S_i*R_i])u=Sum[R_i^T*g_i],<br>> > .. i=1.. to No. of process (subdomains) in parallel.<br>> ><br>> > For the global vector I construct one MPI vector and use VecGetArray ()<br>> for<br>> > each of the sequential vector then use VecSetValues () to add the values<br>> > into the global MPI vector. That works fine.<br>> ><br>> > However for the global schur complement matix I try the same idea by<br>> > creating one parallel MPIAIJ matrix and using MatGetArray( ) and<br>> > MatSetValues () in order to add the values to the global matrix.<br>> > MatGetArray( ) gives me only the values without indices, so I don't know<br>> how<br>> > to add these
valuse to the global MPI matrix.<br>> ><br>> > Thanks agin<br>> ><br>> > Waad<br>> ><br>> > Barry Smith wrote:<br>> ><br>> > On May 20, 2008, at 3:16 PM, Waad Subber wrote:<br>> ><br>> > > Thank you Matt,<br>> > ><br>> > > Any suggestion to solve the problem I am trying to tackle. I want to<br>> > > solve a linear system:<br>> > ><br>> > > Sum(A_i) u= Sum(f_i) , i=1.... to No. of CPUs.<br>> > ><br>> > > Where A_i is a sparse sequential matrix and f_i is a sequential<br>> > > vector. Each CPU has one matrix and one vector of the same size. Now<br>> > > I want to sum up and solve the system in parallel.<br>> ><br>> > Does each A_i have nonzero entries (mostly) associated with one<br>> > part of the matrix? Or does each process have values<br>> > scattered all around the matrix?<br>> ><br>> > In the
former case you should simply create one parallel MPIAIJ<br>> > matrix and call MatSetValues() to put the values<br>> > into it. We don't have any kind of support for the later case, perhaps<br>> > if you describe how the matrix entries come about someone<br>> > would have suggestions on how to proceed.<br>> ><br>> > Barry<br>> ><br>> > ><br>> > ><br>> > > Thanks again<br>> > ><br>> > > Waad<br>> > ><br>> > > Matthew Knepley wrote: On Tue, May 20, 2008 at<br>> > > 2:12 PM, Waad Subber wrote:<br>> > > > Hi,<br>> > > ><br>> > > > I am trying to construct a sparse parallel matrix (MPIAIJ) by<br>> > > adding up<br>> > > > sparse sequential matrices (SeqAIJ) from each CPU. I am using<br>> > > ><br>> > > > MatMerge_SeqsToMPI(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt<br>> > >
n,MatReuse<br>> > > > scall,Mat *mpimat)<br>> > > ><br>> > > > to do that. However, when I compile the code I get the following<br>> > > ><br>> > > > undefined reference to `matmerge_seqstompi_'<br>> > > > collect2: ld returned 1 exit status<br>> > > > make: *** [all] Error 1<br>> > > ><br>> > > > Am I using this function correctly ?<br>> > ><br>> > > These have no Fortran bindings right now.<br>> > ><br>> > > Matt<br>> > ><br>> > > > Thanks<br>> > > ><br>> > > > Waad<br>> > > ><br>> > ><br>> > ><br>> > ><br>> > > --<br>> > > What most experimenters take for granted before they begin their<br>> > > experiments is infinitely more interesting than any results to which<br>> > > their experiments lead.<br>> >
> -- Norbert Wiener<br>> > ><br>> > ><br>> > ><br>> ><br>> ><br>> ><br>> ><br>> ><br>><br>><br>> --<br>> Lisandro Dalcín<br>> ---------------<br>> Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)<br>> Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)<br>> Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)<br>> PTLC - Güemes 3450, (3000) Santa Fe, Argentina<br>> Tel/Fax: +54-(0)342-451.1594<br>><br>><br>><br>><br>><br><br><br>-- <br>Lisandro Dalcín<br>---------------<br>Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)<br>Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)<br>Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)<br>PTLC - Güemes 3450, (3000) Santa Fe, Argentina<br>Tel/Fax: +54-(0)342-451.1594<br><br></w_subber@yahoo.com></blockquote><br><p>