[petsc-users] Best practices for solving Dense Linear systems

[Barry Smith]

> On Aug 6, 2020, at 7:32 PM, Nidish <nb25 at rice.edu> wrote:
> 
> I'm relatively new to PETSc, and my applications involve (for the most part) dense matrix solves.
> 
> I read in the documentation that this is an area PETSc does not specialize in but instead recommends external libraries such as Elemental. I'm wondering if there are any "best" practices in this regard. Some questions I'd like answered are:
> 
> 1. Can I just declare my dense matrix as a sparse one and fill the whole matrix up? Do any of the others go this route? What're possible pitfalls/unfavorable outcomes for this? I understand the memory overhead probably shoots up.

  No, this isn't practical, the performance will be terrible.

> 2. Are there any specific guidelines on when I can expect elemental to perform better in parallel than in serial?

  Because the computation to communication ratio for dense matrices is higher than for sparse you will see better parallel performance for dense problems of a given size than sparse problems of a similar size. In other words parallelism can help for dense matrices for relatively small problems, of course the specifics of your machine hardware and software also play a role.

   Barry

> 
> Of course, I'm interesting in any other details that may be important in this regard.
> 
> Thank you,
> Nidish