[firedrake] operations on matrices

[Colin Cotter]

Oh yes, good isolation of the problem.

If alpha also depends on values of A, do we have a problem there too?

-cjc

On 05/01/15 09:33, David Ham wrote:
> Hi Colin,
>
> There is no way for a parallel loop to read from a matrix. However the
> operation you describe appears to be:
>
> assemble A
> assemble alpha
>
> scale entries of A by the corresponding entries of alpha.
>
> The last step is clearly the problem. I wonder if this could be achieved
> by some PETSc operation on the matrices.
>
> On 5 January 2015 at 09:02, Cotter, Colin J <colin.cotter at imperial.ac.uk
> <mailto:colin.cotter at imperial.ac.uk>> wrote:
>
>     Dear all,
>              Happy New Year!
>
>     Perhaps I made the mistake of making some complex explanation before
>     asking my question.
>
>     What is the best way to make adjustments to matrix entries as part of a
>     loop over elements?
>
>     cheers
>     --cjc
>
>     On 22/12/14 11:13, Cotter, Colin J wrote:
>      > Dear Firedrakers,
>      >    I've been recently revisiting the "algebraic flux correction"
>     schemes
>      > of Dmitri Kuzmin, with the aim of getting a conservative+bounded
>      > advection scheme for temperature in our NWP setup. These schemes
>     involve
>      > the following steps:
>      >
>      > 1) Forming the consistent mass matrix (which is column-diagonal)
>     M_C for
>      > the temperature space.
>      > 2) Constructing the following matrix with the same sparsity as M_C:
>      >
>      > A_{ij} = (M_C)_{ij}(T_i-T_j)
>      >
>      > where T_i is the value of temperature at node i.
>      >
>      > 3) "Limiting" the matrix by replacing
>      >
>      > A_{ij} -> A_{ij}\alpha_{ij}
>      >
>      > where \alpha_{ij} depends on various field values at nodes i and
>     j (only
>      > needs to be evaluated when nodes i and j share an element).
>      >
>      > 4) Evaluating Ax where x is the vector containing 1s, and adding x to
>      > the RHS of mass-matrix projection equation before solving.
>      >
>      > My question is: how to implement this in an efficient and
>     parallel-safe
>      > way in the Firedrake/PyOP2 framework? In particular, step (3)
>     involves
>      > looping over elements, and correcting matrix entries. Also, I'm
>     not sure
>      > of the best way to assemble A.
>      >
>      > all the best
>      > --Colin
>
>
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>
>
>
> --
> Dr David Ham
> Departments of Mathematics and Computing
> Imperial College London
>
> http://www.imperial.ac.uk/people/david.ham
>
>
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