[petsc-users] Fastest solver option after factorization

[Jack Poulson]

Dear Umut,

Since you are interested in the performance of the sparse triangular
solves, I am assuming that you will be performing many such solves
(otherwise the cost would be negligible relative to the factorization).
There is a technique known as "selective inversion" which performs slightly
more work in the factorization, essentially by directly inverting diagonal
blocks, so that the triangular solves can be performed entirely through
dense matrix-vector multiplications.

The main reference for the technique is:
P. Raghavan, "Efficient parallel sparse triangular solution using selective
inversion", Parallel Processing Letters, 8 (1998), no. 1, pp. 29-40.

Here is a reference for the first code to implement the technique (DSCPACK):
P. Raghavan, "Domain-Separator Codes for the parallel solution of sparse
linear systems", Penn State, Technical Report, 2002, CSE-02-004.

I have seen more than an order of magnitude of improvement in one of my
algorithms due to implementing this approach.

Best,
Jack

On Thu, Sep 27, 2012 at 4:48 AM, Umut Tabak <u.tabak at tudelft.nl> wrote:

> Dear all,
>
> I am doing an investigation on the fastest 'Forward backward solver' among
> available sparse direct solvers. I am reading on comparison report, dated
> 2005, namely,
>
> A numerical evaluation of sparse direct solvers for the solution of large
> sparse, symmetric linear systems of equations
>
> N I M Gould, Y Hu, J A Scott
>
> And Pardiso seems to be the best among many solvers. Any further ideas on
> this topic?
>
> I guess this group is one the best lists to ask for opinions ;-)
>
> BR,
> Umut
>
>
>
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