[petsc-users] Interpolation between nodal and elemental field

[K. Wu]

Hi Matt,



I am using two PETSc DM, one for vertices (nodes), and one for cells
(elements).

I want to do the following operation:

x is a global vector generated from DM vertices, with length Nn. y is a
global vector generated from DM cells, with length Ne. I want to generate a
sparse matrix A with size Ne x Nn, so that y = A*x.

The entry of A is set to a constant value, e.g., 1/4, if the corresponding
vertex belongs to the cell.



Hope I make it clear, thanks!



Regards,

Kai

Matthew Knepley <knepley at gmail.com> 于2023年5月16日周二 16:29写道：

> On Tue, May 16, 2023 at 10:27 AM K. Wu <wuktsinghua at gmail.com> wrote:
>
>> Hi all,
>>
>> Good day!
>>
>> I am currently working on interploating the nodal field vector I obtained
>> to its corresponding elemental field vector. I am doing it in a simple way
>> by using structured mesh, the element value is just the average of its
>> corresponding nodal values.
>>
>> Is it possible to generate a connectivity matrix to implement this
>> function? I also need this matrix later on to do a reverse transformation.
>>
>> I am wondering is there a way in PETSc to generate this connectivity
>> matrix between nodal and elemental mesh. Or is there any better way to
>> accomplish this?
>>
>> Thanks for your kind help!
>>
>
> 1. Are you using a PETSc DM, or your own mesh?
>
> 2. In order to define what you mean, you have to attach function spaces
> (or something equivalent) to the
>     two representations. Do you mean linear interpolation between vertices
> and constants on cells?
>
>   Thanks,
>
>      Matt
>
>
>> Best regards,
>> Kai
>>
>
>
> --
> 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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