[petsc-users] Solving hollow matrices

[Barry Smith]

> On Mar 10, 2016, at 4:49 PM, Lucas Clemente Vella <lvella at gmail.com> wrote:
> 
> What PETSc setting of KSP and PC can be used to solve a linear system with matrix with null elements on the main diagonal? Such matrices arise on monolithic methods of solving Navier-Stokes equation.
> 
> I understand it doesn't matter for the KSP method, right?

  Correct
> 
> I know that for lots of PC methods it won't work, like Jacobi or SOR.

  Jacobi just uses a 1 on those entries

> Is there any PC that can handle such matrices?
> 
> For PC method that can't handle hollow matrices, are there any kind of treatment provided by PETSc that can be done to the linear system to ensure  the matrix will have only non-null elements on the main diagonal? Maybe some kind of matrix reordering?

   If the nonzeros "naturally" belong on the diagonal, such as with a Stokes problem then PCFIELDSPLIT is exactly the right preconditioner to use. Take a look at its docs especially using the Schur complement style preconditioners which are often very good for Stokes problems.

   Barry

> 
> -- 
> Lucas Clemente Vella
> lvella at gmail.com