[firedrake] operations on matrices

[Colin Cotter]

Does it help if the matrices are columnwise-blocks? I could assemble the 
entire matrix in a "column kernel" and then perform surgery on it?

--cjc

On 05/01/15 09:39, David Ham wrote:
>
>
> On 5 January 2015 at 09:37, Cotter, Colin J <colin.cotter at imperial.ac.uk
> <mailto:colin.cotter at imperial.ac.uk>> wrote:
>
>     Oh yes, good isolation of the problem.
>
>     If alpha also depends on values of A, do we have a problem there too?
>
>
> Yes. Same problem. There is no current way for a parallel loop to read
> the entries of a matrix.
>
>     -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>
>      > <mailto: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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>
>
> --
> Dr David Ham
> Departments of Mathematics and Computing
> Imperial College London
>
> http://www.imperial.ac.uk/people/david.ham
>
>
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