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