[petsc-users] Number of Blocks in the Block Jacobi preconditionr

[Jed Brown]

On Sun, Sep 23, 2012 at 6:14 PM, Wenlei Xie <wenleix at cs.cornell.edu> wrote:

> Thank you! However as I observed if there are too many blocks (say 200),
> the performance would decrease drastically. Here are some numbers
> (collected under ILU as the preconditioner in the sub block -- I am going
> to test it with LU)
> #Blocks       Setup Time          Solving Time (50 Iterations)
> 100              0.5s       17.5s
> 200    0.76s           19.1s
> 300              2.75s       26.5s
> 500    7.39s                   43.64s
> 1000            39.13s                 165.83s
>
> It looks like both the Setup Time and the Solving Time increase
> significantly as the number of blocks are more than 200. Is this a normal
> result?
>

It does not surprise me. A couple factors

1. Ghost values get copied many times as the subdomains shrink.
2. If you are running in debug mode, there is overhead of going through the
KSP interface for tiny subdomains. The overhead is small in optimized mode
unless there are only a handful of degrees per subdomain. This overhead
would only grow linearly with number of subdomains so it does not explain
your super-linear slow-down.
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