[firedrake] operations on matrices

[David Ham]

On 5 January 2015 at 09:37, Cotter, Colin J <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>> 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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> >     firedrake at imperial.ac.uk <mailto:firedrake at imperial.ac.uk>
> >     https://mailman.ic.ac.uk/mailman/listinfo/firedrake
> >
> >
> >
> >
> > --
> > Dr David Ham
> > Departments of Mathematics and Computing
> > Imperial College London
> >
> > http://www.imperial.ac.uk/people/david.ham
> >
> >
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> > firedrake at imperial.ac.uk
> > https://mailman.ic.ac.uk/mailman/listinfo/firedrake
> >
>
>
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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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