[petsc-users] Efficient MatMatSolve

[Barry Smith]

> On Nov 23, 2016, at 4:57 PM, Łukasz Kasza <rpgwars at wp.pl> wrote:
> 
> Dear PETSc Users,
> 
> I want to compute approximate matrix product A^-1*B where A^-1 is approximated by ILU(0) of A matrix for sequential and parallel executions. For sequential code I can use KSP in preonly mode (PCILU works only for sequential code), get the ILU(0) by PCFactorGetMatrix and then call MatMatSolve. However the resulting matrix has to be in dense format because that's the way MatMatSolve works. In my case A^-1*B product is sparse for sure, because ILU(0) has the same sparsity pattern.

   Even though your ILU(0) factorization of A is sparse the resulting A^-1*B will almost surely be dense since the triangular solves"fill" in the column vector entries in the result.

> Suppose that I 
> will have a factored A matrix for parallel code as well. What is the best way to get the A^-1*B product without creating dense matrices? Is it even possible? 

  Why do you want to form A^-1*B? Or do you want to just use A^-1*B in some other computation? Perhaps that can be done "matrix" free by not forming A^-1*B but instead doing matrix vector products of A^-1*B  which will be cheap if you have an ILU(0) of A.

   Barry

> 
> Best Regards,
> Damian Goik
> 
> 
>