[petsc-users] Solving A*X = B where A and B are matrices

[Barry Smith]

http://www.mcs.anl.gov/petsc/documentation/faq.html#computers

On Dec 3, 2012, at 1:08 PM, Jelena Slivka <slivkaje at gmail.com> wrote:

> Thank you very much! 
> However, I have another question. I have a cluster of 4 nodes and each node has 6 cores. If I run my code using 6 cores on one node (using the command "mpiexec -n 6") it is much faster than running it on just one process (which is expected). However, if I try running the code on multiple nodes (using "mpiexec -f machinefile -ppn 4", where machinefile is the file which contains the node names), it runs much slower than on just one process. This also happens with tutorial examples. I have checked the number of iteration for KSP solver when spread on multiple processors and it doesn't seem to be the problem. Do you have any suggestions on what am I doing wrong? Are the commands I am using wrong?
> 
> 
> On Sat, Dec 1, 2012 at 6:03 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
>     We recommend following the directions http://www.mcs.anl.gov/petsc/documentation/faq.html#schurcomplement  for computing a Schur complement; just skip the unneeded step. MUMPS supports a parallel Cholesky but you can also use a parallel LU with MUMPS, PaSTIX or SuperLU_Dist and those will work fine also. With current software Cholesky in parallel is not tons better than LU so generally not worth monkeying with.
> 
>    Barry
> 
> 
> On Dec 1, 2012, at 12:05 PM, Jelena Slivka <slivkaje at gmail.com> wrote:
> 
> > Hello!
> > I am trying to solve A*X = B where A and B are matrices, and then find trace of the resulting matrix X. My approach has been to partition matrix B in column vectors bi and then solve each system A*xi = bi. Then, for all vectors xi I would extract i-th element xi(i) and sum those elements in order to get Trace(X).
> > Pseudo-code:
> > 1) load matrices A and B
> > 2) transpose matrix B (so that each right-hand side bi is in the row, as operation MatGetColumnVector is slow)
> > 3) set up KSPSolve
> > 4) create vector diagonal (in which xi(i) elements will be stored)
> > 5) for each row i of matrix B owned by current process:
> >           - create vector bi by extracting row i from matrix B
> >           - apply KSPsolve to get xi
> >           - insert value xi(i) in diagonal vector (only the process which
> >             holds the ith value of vector x(i) should do so)
> > 6) sum vector diagonal to get the trace.
> > However, my code (attached, along with the test case) runs fine on one process, but hangs if started on multiple processes. Could you please help me figure out what am I doing wrong?
> > Also, could you please tell me is it possible to use Cholesky factorization when running on multiple processes (I see that I cannot use it when I set the format of matrix A to MPIAIJ)?
> >
> > <Experiment.c><Abin><Bbin>
> 
>