Re: [firedrake] operations on matrices
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@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
_______________________________________________ firedrake mailing list firedrake@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
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@imperial.ac.uk <mailto:colin.cotter@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
_______________________________________________ firedrake mailing list firedrake@imperial.ac.uk <mailto:firedrake@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
_______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake
On 5 Jan 2015, at 09:37, Colin Cotter <colin.cotter@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?
Note, FWIW, that petsc doesn't offer a nice way of computing the Hadamard product. Lawrence
participants (3)
-
Colin Cotter
-
David Ham
-
Lawrence Mitchell