# [petsc-users] Parallel dense solve with submatrices

Toon Weyens weyenst at gmail.com
Mon Aug 28 03:15:03 CDT 2017

```Thank you Barry, that explains why I couldn't find information about it. I
am now going to implement this straight-forward implementation as a first
step.

In the long term it would in any case be useful to have a solver that uses
H-matrices, such as H2lib.

Is there any chance Petsc is thinking about moving to this kind of matrices
as well in the future?

On Sun, Aug 27, 2017 at 12:54 AM Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>   Toon,
>
>    We don't have any such way of doing this. Note that sparse
> factorization packages store the "factors" in specialized data structures
> that are unlikely to be acessable to perform such operations as you
> describe below.
>
>    I think what you want to do is an over optimization not worth the
> coding effort.
>
>   Barry
>
> > On Aug 25, 2017, at 5:01 AM, Toon Weyens <weyenst at gmail.com> wrote:
> >
> > Dear all,
> >
> > For a Bounday Element Method problem I require the solution of a system
> of linear equations with multiple right-hand sides. Though this is a dense
> system, I still want to do it via Petsc. Would the best way to do this be
> through something such as
> >
> > -ksp_type preonly -pc_type lu -pc_factor_mat_solver_package mumps  ?
> >
> > Furthermore, I refine my grid in a regular way, which leads to a new
> system of equations of size 2N x 2N where N is the original number of
> unknowns before refining it. The upper-left matrix A_11 in this new system
> is identical to the unrefined matrix (multiplied by 0.5). The other three
> blocks A_12, A_21 and A_22 are new:
> >
> >        A_11 A_12
> >        A_21 A_22
> >
> > The question is now whether knowledge about the unrefined matrix A_11
> can be used to speed up calculation of the refined system?
> >
> > I was thinking, for example, about using the LU decomposition of A_11 to
> calculate the LU decomposition of the entire matrix A using the well-known
> formula's
> >
> > L_21 U_11 = A_21
> > L_11 U_12 = A_12
> > L_22 U_22 = A_22 - L_21 U_12
> >
> > where L_21 and U_12 are full matrices, L_11, L_22 are lower triangular
> matrices and U_11, U_22 are upper triangular.
> >
> > Is there any way to do this in Petsc?
> >
> > Or is there a better thing I can do?
> >
> > Thanks very much in advance!
> >
> > Regards.
> >
> > Dr. Toon Weyens
> > ITER Organization
>
>
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