[petsc-users] Yet another inversion question

[Barry Smith]

   Umut,

     You do not want to use MatGetColumnVector() on a sparse matrix it  
is very slow.

     Follow the directions at http://www.mcs.anl.gov/petsc/petsc-as/documentation/faq.html#invertmatrix 
  in your case don't use the identity for B but use your B as a dense  
matrix.

     For applying many rows, a direct solver will always win over  
using an iterative solver for each column.


     Barry

On May 1, 2010, at 3:27 PM, Umut Tabak wrote:

> Dear all,
>
> I need some terms in my algorithm such as
>
> A^{-1} B
>
> so and inverted matrix multiplied by another one(A and B pretty  
> sparse, however inversion makes all the sparsity lost). Explicit  
> inverse is not the way to go, however I thought of solving for the  
> columns of B thorugh KSP and put them into another matrix as  
> columns(which might be expensive as well I am not sure)and  
> eventually I will get the term I would like. I know these kinds of  
> terms should be avoided if possible but for the moment I can not  
> avoid them so what would be the best way to compute this dense  
> symmetric resulting matrix.
>
> I did a  first try to  solve for the columns of B, with the umfpack  
> interface and direct solve, which seemed to be fastest on a matrix  
> of size 5544( to  solve for all the columns of B). About 1m11sec. to  
> do the above mentioned solves. I was wondering if there some more  
> efficient ways to make this operation faster than what I could  
> accomplish now. Otherwise I should leave this way of thinking.
> Sth like,
>
> for(PetscInt indx=0; indx<c; indx++)
> {
>   //cout << "Column : "  << indx << endl;
>   // retrieve column
>   MatGetColumnVector(Mss, u, indx);
>   /*        Solve linear system
>   */
>   ierr = KSPSolve(ksp,u,x);CHKERRQ(ierr);
> }
>
> Best regards,
> Umut
>
>
>
>
>