[firedrake] operations on matrices

[Colin Cotter]

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