[petsc-users] How to use MatSetValuesStencil() with DOF>1

[Matthew Knepley]

On Fri, May 29, 2020 at 12:16 PM Lucas Banting <bantingl at myumanitoba.ca>
wrote:

> Hello,
>
> I have a structured grid problem with 5 unknowns per cell: U,V,P,T,F, this
> is a CFD code but I don't think these details are necessary to answer my
> question.
> I was wondering how exactly I should use MatSetValuesStencil() to fill my
> matrix.
> I have 5 degrees of freedom, so I need to set up to 25 coefficients per
> grid cell. I don't understand how i,j, and c map to all coefficients.
>
> For a 1 degree of freedom system to fill my 9 point stencil I did:
>
>           values(1)= ASW(II,JJ)
>           values(2)= AS (II,JJ)
>           values(3)= ASE(II,JJ)
>           values(4)= AW (II,JJ)
>           values(5)= AP (II,JJ)
>           values(6)= AE (II,JJ)
>           values(7)= ANW(II,JJ)
>           values(8)= AN (II,JJ)
>           values(9)= ANE(II,JJ)
>
>           idxm(MatStencil_i,1) = II;idxm(MatStencil_j,1) = JJ
>
>           idxn(MatStencil_i,1) = II-1;idxn(MatStencil_j,1) = JJ-1
>           idxn(MatStencil_i,2) = II    ;idxn(MatStencil_j,2) = JJ-1
>           idxn(MatStencil_i,3) = II+1;idxn(MatStencil_j,3) = JJ-1
>           idxn(MatStencil_i,4) = II-1 ;idxn(MatStencil_j,4) = JJ
>           idxn(MatStencil_i,5) = II    ;idxn(MatStencil_j,5) = JJ
>           idxn(MatStencil_i,6) = II+1;idxn(MatStencil_j,6) = JJ
>           idxn(MatStencil_i,7) = II-1 ;idxn(MatStencil_j,7) = JJ+1
>           idxn(MatStencil_i,8) = II     ;idxn(MatStencil_j,8) = JJ+1
>           idxn(MatStencil_i,9) = II+1;idxn(MatStencil_j,9) = JJ+1
>           call
> MatSetValuesStencil(A,1,idxm,9,idxn,values,INSERT_VALUES,ierr)
>
> Which seemed to work just fine. For 5 degrees of freedom, instead of just
> having a single AP coefficient for example, I have an AP matrix:
>
> ap_uu
> ap_uv
> ap_up
> ap_ut
> ap_uf
> ap_vu
> ap_vv
> ap_vp
> ap_vt
> ap_vf
> ap_pu
> ap_pv
> ap_pp
> ap_pt
> ap_pf
> ap_tu
> ap_tv
> ap_tp
> ap_tt
> ap_tf
> ap_fu
> ap_fv
> ap_fp
> ap_ft
> ap_ff
>
> In 1 degree of freedom, i and j corresponded to the solution variable in
> the grid. For multi degree of freedom, I don't understand how values of i,
> j, and c could distinguish from an ap_uv and ap_vv coefficent for example,
> wouldn't they both be at i, j ,c=2?
> Is there anyway I can use MatSetValuesStencil() to fill in my 9 point
> stencil with my 5x5 matrix coefficients? To clarify I have nine 5x5
> matrices for each cell which correspond to the 5 unknowns per cell.
>

In MatSetValuesStencil(), I think it is best to think of the Stencils as
another way of providing row/col numbers. So each MatStencil corresponds
to some row number. So your ap_uv is some entry in the input matrix, and
thus corresponds to some row number (a MatStencil) and some
column number (another MatStencil). Since ap is one point, it appears that

  ap_uv --> row = i,j,0   col = i,j,1
  ap_vv --> row = i,j,1   col = i,j,1

So you line up your MatStencil arguments to match the order of your input.
It sounds like you want the field index to be the fastest in your input.

Does that make sense?

  Thanks,

     Matt



> Thanks,
>
> Lucas
>


-- 
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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