[Trilinos-Users] Sparse direct solver and language options for GPU

[Tom Anderson]

Chetan,

Thanks for the reference! This paper describes my problem exactly.

I think my problem meets all five of the criteria C1-C5 in the paper.

In my problem the top left mxm block (A block in the paper) is much larger
and more complex that the nxn block (B block in the paper).

Unless anyone has an easier suggestion, I will try both of your suggested
approaches and see which one
works better.

Do you have a references or any suggestions with more details on how to
proceed with Trilinos to implement either of these approaches?

Thanks again,

-Tom

On Thu, Sep 18, 2014 at 11:50 AM, Chetan Jhurani <chetan.jhurani at gmail.com>
wrote:

> Tom,
>
>
>
> From the example you gave, the matrix looks like a “saddle point system”,
>
> which is a natural matrix form in many problems.  The matrix will not
>
> be semi-definite in this case but it will be indefinite.  Hence you saw the
>
> warning about negative eigenvalue.  It will be useful to take advantage
>
> of the structure of saddle point matrices (whether Trilinos is used or
> cholmod).
>
>
>
> I’m no expert here but you might benefit from elimination of extra
> variables since
>
> it looks like the constraints are very simple (v_b - v_a = V1 etc).  After
> elimination,
>
> you could use a solver/preconditioner pair that works well with positive
>
> definite matrices.  The other approach is to “solve” the m x m portion
> rather than
>
> going for the full (m+n) x (m+n) matrix.  The right choice depends on the
> relative
>
> sizes of m and n and the simplicity of the “constraint” block vs the
> simplicity
>
> of the top-left m x m block.
>
>
>
> Consult the following popular paper if you want to solve saddle point
> problems
>
> by either of these approaches.
>
> http://web.stanford.edu/class/msande312/restricted/benzi05saddle.pdf
>
> Numerical solution of saddle point problems
>
>
>
> Chetan
>
>
>
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