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

[Stefano Zampini]

Here you have an example of a 2 dof system using MatSetValuesBlockedStencil

https://github.com/stefanozampini/petscopt/blob/master/src/ts/examples/tests/ex3.c#L186 <https://github.com/stefanozampini/petscopt/blob/master/src/ts/examples/tests/ex3.c#L186>

> On May 29, 2020, at 8:55 PM, Lucas Banting <bantingl at myumanitoba.ca> wrote:
> 
> Yes, I think that makes sense to me. Each cell is at i,j but then you can set the 25 coefficients per node using MatStencil_c from 0 to 4 for both idxm and idxn.
> 
> Thanks for your help.
> 
> Lucas
> From: Matthew Knepley <knepley at gmail.com>
> Sent: Friday, May 29, 2020 12:47 PM
> To: Lucas Banting <bantingl at myumanitoba.ca>
> Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] How to use MatSetValuesStencil() with DOF>1
>  
> On Fri, May 29, 2020 at 12:16 PM Lucas Banting <bantingl at myumanitoba.ca <mailto: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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