[petsc-users] Matvecs and KSPSolves with multiple vectors

[Sreeram R Venkat]

Thank you Barry and Pierre; I will proceed with the first option.

I want to use the AMGX preconditioner for the KSP. I will try it out and
see how it performs.

Thanks,
Sreeram

On Thu, Dec 7, 2023 at 2:02 PM Pierre Jolivet <pierre at joliv.et> wrote:

> To expand on Barry’s answer, we have observed repeatedly that MatMatMult
> with MatAIJ performs better than MatMult with MatMAIJ, you can reproduce
> this on your own with https://petsc.org/release/src/mat/tests/ex237.c.html
> .
> Also, I’m guessing you are using some sort of preconditioner within your
> KSP.
> Not all are “KSPMatSolve-ready”, i.e., they may treat blocks of right-hand
> sides column by column, which is very inefficient.
> You could run your code with -info dump and send us dump.0 to see what
> needs to be done on our end to make things more efficient, should you not
> be satisfied with the current performance of the code.
>
> Thanks,
> Pierre
>
> On 7 Dec 2023, at 8:34 PM, Barry Smith <bsmith at petsc.dev> wrote:
>
>
>
> On Dec 7, 2023, at 1:17 PM, Sreeram R Venkat <srvenkat at utexas.edu> wrote:
>
> I have 2 sequential matrices M and R (both MATSEQAIJCUSPARSE of size n x
> n) and a vector v of size n*m. v = [v_1 , v_2 ,... , v_m] where v_i has
> size n. The data for v can be stored either in column-major or row-major
> order.  Now, I want to do 2 types of operations:
>
> 1. Matvecs of the form M*v_i = w_i, for i = 1..m.
> 2. KSPSolves of the form R*x_i = v_i, for i = 1..m.
>
> From what I have read on the documentation, I can think of 2 approaches.
>
> 1. Get the pointer to the data in v (column-major) and use it to create a
> dense matrix V. Then do a MatMatMult with M*V = W, and take the data
> pointer of W to create the vector w. For KSPSolves, use KSPMatSolve with R
> and V.
>
> 2. Create a MATMAIJ using M/R and use that for matvecs directly with the
> vector v. I don't know if KSPSolve with the MATMAIJ will know that it is a
> multiple RHS system and act accordingly.
>
> Which would be the more efficient option?
>
>
> Use 1.
>
>
> As a side-note, I am also wondering if there is a way to use row-major
> storage of the vector v.
>
>
> No
>
> The reason is that this could allow for more coalesced memory access when
> doing matvecs.
>
>
>   PETSc matrix-vector products use BLAS GMEV matrix-vector products for
> the computation so in theory they should already be well-optimized
>
>
> Thanks,
> Sreeram
>
>
>
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