[petsc-users] support for mixed block size matrices/AIM in PETSc?

[Matthew Knepley]

On Mon, Jul 24, 2023 at 6:34 AM Daniel Stone <daniel.stone at opengosim.com>
wrote:

> Hello PETSc Users/Developers,
>
> A collegue of mine is looking into implementing an adaptive implicit
> method (AIM) over
> PETSc in our simulator. This has led to some interesting questions about
> what can
> be done with blocked matrices, which I'm not able to answer myself - does
> anyone have
> any insight?
>
> Apparently it would be ideal if we could find a matrix (and vector) type
> that supports a kind
> of mixed block size:
>
> "For AIM [...] we will have matrix elements of various shapes: 1x1, 1xN,
> Nx1 and NxN. [...]. The solution and residual will be a mix of 1 and N
> variable/cell block"
>

This is not the terminology we would use, since "blocksize" is usually
understood as something small
that is used for vectorization and indexing. These are large, O(N), and
require different implementation.
To build matrices out of these parts, you can use

  1) MatNest: Very small blocks are not ideal here, so

  2) MatLRC: This is for low-rank corrections, which is where small
matrices tend to arise

Does this make sense?

  Thanks,

    Matt


> There are ideas for how to implement what we want using the
> fixed-block-size objects we
> understand well, but if anything like the above exists it would be very
> exciting.
>
>
> Thanks,
>
> Daniel
>


-- 
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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