[petsc-users] Yet another inversion question

[Umut Tabak]

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