[petsc-users] tridiagonal matrix in kspsolve

[Jed Brown]

Shriram Srinivasan <shriram at ualberta.ca> writes:

> Apologies if my question  is answered elsewhere already. I could not 
> find this discussed in the manual or mailing list.
>
> I have been using matsolvermumps through ksp to solve my linear system. 
> I wanted to simply get it working so I was not concerned about the 
> structure of the matrix.
>
>
> 1) My matrix is tridiagonal, but the elements of the diagonals are not 
> all equal.  Will a dedicated tridiagonal solver   be faster than 
> matsolvermumps in this case ?
>
> 2) My matrix is tridiagonal but not in the conventional sense, the minor 
> diagonals are farther apart. But it is possible to renumber the nodes 
> and make it a conventional tridiagonal system. In this case, again, am I 
> losing efficiency using matsolvermumps ?

Yes on all counts, but use a profiler to see where the time is spent.  A
good implementation will specialize the tridiagonal structure and
aggregate all the problems.  It can be done efficiently, but I'm not
aware of general-purpose libraries.

However, I reiterate my earlier statements that ADI is an antiquated
method that has fallen out of favor since it is a poor parallel
algorithm and has large splitting errors.
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