Re: PETSc jacobian

["Matthew Knepley" <knepley@xxxxxxxxx>]

On 3/6/07, Jianing Shi <jianings@xxxxxxxxx> wrote:
> Hi PETSc designers,
>
> I have a non-trivial extension to a diffusion problem, that involves
> talking between neighboring (neighboring band) points.  I have a
> question about the data structures in PETSc, since I am fantasized
> about elegant designs.
>
> I have two options: 1) use structured grid (DA)   2) in some
> applications, my grid can be unstructured, in fact a directed graph.
> I am considering the first option now (since I still need to read up
> onto the PETSc mesh/graph).
>
> Suppose I need to represent the connectivity of a point to its
> neighboring points, I need a weight matrix.  I guess I can
> (A) use a DA structure, setting DOF = total number of points connected
> to a point (assuming the connectivity range for each point is the
> same).
> or
> (B) use a Jacobian matrix data structure to store these weights.  In
> this case, I guess I will use MATMPIAIJ or MATMPIBAIJ.
>
> - What is the difference between these two types of Jacobian matrix?

One has a fixed Cartesian topology (connectivity). The other can have
an arbitrary connectivity.

> - For distributed sparse matrix like MATMPIAIJ, MATMPIBAIJ, how
> efficient is it to extract one column of the matrix M(i,:) ?  Does
> PETSc have routines to do this?

It is there, but it is not efficient. Row extraction is efficient.

> - How is such a distributed sparse matrix stored on different
> processors, how is it divided up, and collected?

Row-wise. There is a picture in the manual.

> I want to understand this, because if a distributed sparse matrix is
> an efficient representation of my sparse weight matrix, I will go for
> this option (B).  Otherwise, I will opt for option (A).

I think you are confusing two issues. The DA is not an operator or a matrix.
it is a topology or connectivity. It can create an AIJ matrix with that
connectivity automatically.

 Matt

> Thanks!
>
> Jianing


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