[petsc-users] Efficient Block Matrix implementation

[Matthew Knepley]

On Fri, Apr 27, 2012 at 3:50 PM, <tibo at berkeley.edu> wrote:

> Hi,
>
> I am using petsc in a Fortran code to solve large systems of linear
> equations Ax = b where A is a matrix resulting from a discretization of a
> reaction diffusion problem: A is block-tridiagonal, and each of the three
> blocks is sparse. It turns out that I know exactly the sparsity structure
> of each block (ie the number and position of non-zeros per row).
>
> For now, I am only writing a sequential code. From the petsc manual, it
> seems there are two ways to create my matrix A: Either using
> MatCreateSeqAIJ, or using MatCreateSeqBAIJ. The second approach seems
> recommended since A is indeed a Block matrix.
>

No, I think you just want AIJ. BAIJ is for matrices made of small dense
blocks in
a sparse pattern, not big sparse blocks in a dense pattern.

   Matt


> However, the command MatCreateSeqAIJ allows me to specify the number of
> non zeros per row, therefore allowing me to take advantage of knowing the
> sparsity structure of my blocks (but losing the advantage of using the
> fact that the matrix is a block matrix). It seems that the command
> MatCreateSeqBAIJ only allows me to specify the number of non zeros blocks
> per block rows, therefore losing the available information on the sparsity
> of each block.
>
> My question is then: Is there a way to declare the matrix to take
> advantage of both the fact that my matrix is a block matrix (or even
> better, that it is a block tridiagonal matrix) and that I know the
> sparsity structure of the blocks ?
>
> I am asking this question because If I use the block matrix approach as
> described above (just specifying the number of non zeros blocks per block
> rows) versus the AIJ approach with specifying the number of non zeros for
> each row, the computing time increases by a factor of 5, every other
> parameters being unchanged.
>
> Thank you
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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