[petsc-users] need help with vector interpolation on nonuniform DMDA grids

[Matthew Knepley]

On Tue, Nov 6, 2018 at 5:11 AM Francesco Magaletti via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear all,
>
> I would like to ask you if is there an easy and efficient way in parallel
> (by using PetsC functions) to interpolate a DMDA vector associated with a
> nonuniform 1D grid to another DMDA vector with the same length but
> associated with a different nonuniform grid.
>
> Let me rephrase it to be as clearer as I can:
>
> I have two structured nonuniform 1D grids with coordinate vectors x[i] and
> y[i]. Both the domains have been discretized with the same number of
> points, but the coordinate vectors x and y are different. I have a
> discretized field u[i] = u(x[i]) and I would like to use these point values
> to evaluate the values u(y[i]) in the points of the second grid.
>
> I read on the manual pages that functions like DMCreateInterpolation or
> similar work only with different but uniform DMDAs. Did I understand
> correctly?
>
> A naive approach, with a serial code, could be to find the points x[i] and
> x[i+1] that surround the point y[j] for every j and then simply linear
> interpolating the values u[i] and u[i+1]. I suspect that this is not the
> most efficient way to do it. Moreover it won’t work in parallel since, in
> principle, I do not know beforehand how many ghost nodes could be necessary
> to perform all the interpolations.
>
> Thank you in advance for your help!
>

This has not been written, but is not that hard. You would first bin the
points into cells, and then use the
interpolant from the discretization. This is how we do it in the
unstructured case. Actually, if you wrote
your nonuniform 1D meshes as DMPlexes, I think it would work right now
(have not tested).

  Thanks,

   Matt


> Francesco



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