[petsc-users] Question about matrix permutation

Barry Smith bsmith at mcs.anl.gov
Fri Jan 29 13:48:57 CST 2010

On Jan 29, 2010, at 11:29 AM, Michel Cancelliere wrote:

> Thank you for your promptly response,  i will use unsorted inex set as
> you suggest (because my submatrices are very large (4 submatrices N/2
> x N/2 from the original one Nx N),
> I realize that i cannot use block matrices because the reordering
> split within the blocks and the resulting matrices are not block
> matrices anymore. In terms of performance how much can affect this to
> the code, in the sense if i apply for example an ILU preconditioner to
> a block matrix (baij) and solve the same system but this time using an
> aij matrix ? not sure if it is clear

    It is not clear what you are asking.

    **If you have a matrix with say block size of 4 and store it with  
BAIJ and do factorizations and solvers and it takes N seconds then  
solve the same system with factorization and solvers with AIJ it will  
take at least 1.5 * N seconds. The block BAIJ format uses a point  
block ILU factorization so usually gives better convergence rate than  
AIJ depending on the problem.

   But you state that the submatrix you select does not have the same  
block structure so my answer ** is irrelevent. In general using a  
smart composite preconditioner (as Jed is taking about with  
PCFiledSplit or friends) is better then using a dumb global  
preconditioner like ILU(0) on the whole problem. Yes, the flop rate  
may be lower because you cannot do block ILU on the BAIJ matrix but  
there should be so fewer flops because of the better preconditioner  
that the smart preconditioner wins. If the smart preconditioner does  
not win then it is not a smart preconditioner for the problem :-)


> Thanks
> Michel
> On 1/29/10, Jed Brown <jed at 59a2.org> wrote:
>> On Fri, 29 Jan 2010 09:43:05 -0600 (CST), abhyshr at mcs.anl.gov wrote:
>>> Instead of calling MatGetSubMatrix to get each submatrix you can use
>>> MatGetSubMatrices to extract several submatrices at once. See
>>> http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/Mat/MatGetSubMatrices.html#MatGetSubMatrices 
>>> .
>> I don't think Michel was asking to extract multiple matrices.  In
>> serial, MatGetSubMatrices is implemented by calling MatGetSubMatrix  
>> so
>> there is no weaker assumption on index set sortedness.
>> Jed

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