[petsc-users] Setting up MUMPS in PETSc

[Jed Brown]

On Tue, Oct 23, 2012 at 2:36 PM, Jinquan Zhong <jzhong at scsolutions.com>wrote:

> *>> That is a good point.  In these applications, we don’t usually have a
> good-conditioned matrix . The condition number is always around
> 10^10--10^12.  This is out of our control.*
>

This is something you may have to "take control" of if you want accurate
solutions. You can also compute in quad precision
(--with-precision=__float128), but AFAIK, there are no quad-precision
distributed memory sparse direct solvers.


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> Is this the reason you want to use a direct solver instead of iterative
> one?****
>
> What do you mean "31k with a dense matrix included in the sparse matrix"?*
> ***
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> *>> We have a dense matrix embedded inside a sparse matrix.  This dense
> matrix usually accounts for 99% of the total nnz’s.*
>

What does that dense coupling represent?


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> How sparse is your matrix, e.g., nnz(A)/(m*m)=?****
>
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> *>> ~=0.4% for medium size problem and 0.04% for large size problem.*
>

Uhh, your numbers for the large problem are 178k^2 / 640k^2 = 7.8%.


> Both a and b seem indicate that, you can use small num of cores to
> generate original matrix A, but need more cores (resource) to solve A x =b.
>
> **
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> *>> My confusion is that since the sparse matrix size is the same, why
> resource for 1152 cores are needed for 576 partitions on A, while only
> resource for 432 cores are needed for 144 partitions on A?  If using 432
> cores can solve the 144- partition Ax=b, why did it need 1152 cores to
> solve 576-partition Ax=b?  I expected 576 cores could do the job that 432
> cores did on the 576-partition Ax=b.*
>

The amount of fill depends on the size of minimal vertex separators. Sparse
matrices with the same number of nonzeros and same number of nonzeros per
row can have vertex separators that are orders of magnitude different in
size. The fill is quadratic in the size of the separators and computation
is cubic.


Is your problem symmetric?
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