[petsc-users] Advice on small block matrix vector multiplication

[Duan Junming]

From: knepley at gmail.com <knepley at gmail.com>
Sent: Sunday, June 18, 2023 20:35
To: Duan Junming
Cc: petsc-users at mcs.anl.gov
Subject: Re: [petsc-users] Advice on small block matrix vector multiplication

On Sun, Jun 18, 2023 at 2:13 PM Duan Junming via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
Dear all,

I am using DMPlex to manage the unknowns, two fields, one for pressure, and one for velocities with two/three components, defined in each cell. They're represented by polynomials, with N (10~50) dofs for each component.
I have an operator which can be written in a matrix form (N-by-N, dense), to be applied on the pressure field or each component of the velocities in each cell (the same for each cell and also for each component).
I was wondering which matrix should be defined to implement the block matrix-vector multiplication, here block means the pressure or the component of the velocities. Maybe a sequential block mat? Could you recommend any example?
Or I just implement this matrix-vector multiplication by hand?

Dear Matt,

Thank you for your quick reply!

1) It sounds like you have a collocated discretization, meaning p,u,v,w are all at the same spots. Is this true?

You're right. They're collocated at the same position.

2) You have a dense operator, like FFT, that can act on each component

Right, a dense operator applied on each component.

3) I think you should make a vector with blocksize d+1 and extract the components with

  https://petsc.org/main/manualpages/Vec/VecStrideGather/

then act on them, then restore with

  https://petsc.org/main/manualpages/Vec/VecStrideScatter/

You can use the *All() versions to do all the components at once.

Does this function work with the global/local vector generated from DMPlex? Now the vector is like: p_1, p_2, ..., p_N, u_1, v_1, w_1, ..., u_N, v_N, w_N.

  Thanks,

     Matt

Thanks!
Junming


--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
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