Multilevel solver

[Matthew Knepley]

On Thu, Apr 24, 2008 at 8:58 AM,  <Amit.Itagi at seagate.com> wrote:
> Barry,
>
>  I have been trying out the PCFIELDSPLIT. I have not yet gotten it to work.
>  I have some follow up questions which might help solve my problem.
>
>  Consider the simple case of a 4x4 matrix equation being solved on two
>  processes. I have vector elements 0 and 1 belonging to rank 0, and elements
>  2 and 3 belonging to rank 1.
>
>  1) For my example, can the index sets have staggered indices i.e. is1-> 0,2
>  and  is2->1,3  (each is spans across ranks) ?

Yes.

>  2) When I provide the -field_split_<n>_pc_type option on the command line,
>  is the index <n> in the same order that the PCFieldSplitSetIS function
>  called in ?
>      So if I have  PCFieldSplitSetIS(pc,is2) before
>  PCFieldSplitSetIS(pc,is1), will -field_split_0_... correspond to is2 and
>  -field_split_1_... to is1 ?

Yes.

>  3) Since I want to set PC type to lu for field 0, and I want to use MUMPS
>  for parallel LU, where do I set the submatrix type to MATAIJMUMPS ? In this
>  case, will a second copy of the submatrix be generated - one of type MUMPS
>  for the PC and the other of the original MATAIJ type for the KSP ?

I will have to check. However if we are consistent, then it should be

  -field_split_0_mat_type aijmumps

>  4) How is the PC applied when I do PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE ?

It is just the composition of the preconditioners, which is what you want here.

  Matt

>  Thanks
>
>  Rgds,
>  Amit
>
>
>
>
>              Barry Smith
>              <bsmith at mcs.anl.g
>              ov>                                                        To
>              Sent by:                  petsc-users at mcs.anl.gov
>              owner-petsc-users                                          cc
>              @mcs.anl.gov
>              No Phone Info                                         Subject
>              Available                 Re: Multilevel solver
>
>
>              04/22/2008 10:08
>              PM
>
>
>              Please respond to
>              petsc-users at mcs.a
>                   nl.gov
>
>
>
>
>
>
>   Amit,
>
>      Using a a PCSHELL should be fine (it can be used with GMRES),
>  my guess is there is a memory corruption error somewhere that is
>  causing the crash. This could be tracked down with www.valgrind.com
>
>     Another way to you could implement this is with some very recent
>  additions I made to PCFIELDSPLIT that are in petsc-dev
>  (http://www-unix.mcs.anl.gov/petsc/petsc-as/developers/index.html)
>  With this you would chose
>  PCSetType(pc,PCFIELDSPLIT
>  PCFieldSplitSetIS(pc,is1
>  PCFieldSplitSetIS(pc,is2
>  PCFieldSplitSetType(pc,PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE
>  to use LU on A11 use the command line options
>  -fieldsplit_0_pc_type lu -fieldsplit_0_ksp_type preonly
>  and SOR on A22
>  -fieldsplit_1_pc_type sor -fieldsplit_1_ksp_type preonly -
>  fieldsplit_1_pc_sor_lits <lits> where
>     <its> is the number of iterations you want to use block A22
>
>  is1 is the IS that contains the indices for all the vector entries in
>  the 1 block while is2 is all indices in the
>  vector for the 2 block. You can use ISCreateGeneral() to create these.
>
>    Probably it is easiest just to try this out.
>
>    Barry
>
>
>  On Apr 22, 2008, at 8:45 PM, Amit.Itagi at seagate.com wrote:
>
>  >
>  > Hi,
>  >
>  > I am trying to implement a multilevel method for an EM problem. The
>  > reference is : "Comparison of hierarchical basis functions for
>  > efficient
>  > multilevel solvers", P. Ingelstrom, V. Hill and R. Dyczij-Edlinger,
>  > IET
>  > Sci. Meas. Technol. 2007, 1(1), pp 48-52.
>  >
>  > Here is the summary:
>  >
>  > The matrix equation Ax=b is solved using GMRES with a multilevel
>  > pre-conditioner. A has a block structure.
>  >
>  > A11    A12       *         x1  =  b1
>  > A21    A22                  x2       b2
>  >
>  > A11 is mxm and A33 is nxn, where m is not equal to n.
>  >
>  > Step 1  :      Solve  A11 *  e1   = b1     (parallel LU using
>  > superLU or
>  > MUMPS)
>  >
>  > Step 2:        Solve   A22 * e2    =b2-A21*e1    (might either user
>  > a SOR
>  > solver or a parallel LU)
>  >
>  > Step 3:        Solve   A11* e1 = b1-A12*e2   (parallel LU)
>  >
>  > This gives the approximate solution to
>  >
>  > A11     A12     *      e1   =  b1
>  > A21     A22             e2       b2
>  >
>  > and is used as the pre-conditioner for the GMRES.
>  >
>  >
>  > Which PetSc method can implement this pre-conditioner ? I tried a
>  > PCSHELL
>  > type PC. With Hong's help, I also got the parallel LU to work
>  > withSuperLU/MUMPS. My program runs successfully on multiple
>  > processes on a
>  > single machine. But when I submit the program over multiple
>  > machines, I get
>  > a crash in the PCApply routine after several GMRES iterations. I
>  > think this
>  > has to do with using PCSHELL with GMRES (which is not a good idea). Is
>  > there a different way to implement this ? Does this resemble the usage
>  > pattern of one of the AMG preconditioners ?
>  >
>  >
>  > Thanks
>  >
>  > Rgds,
>  > Amit
>  >
>
>
>
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
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