# Matrix convergence.

Matthew Knepley knepley at mcs.anl.gov
Thu Mar 2 16:22:04 CST 2006

```billy at dem.uminho.pt writes:

> Yes, it is elliptic.

Then this does not make a lot of sense. However, it looks like
it is nonsymmetrix, so maybe severe non-normality is screwing up
the solve. I would export to Matlab and plot the spectrum of both
the operator and the preconditioned operator since the matrix is
small enough.

Matt

> Quoting Matthew Knepley <knepley at mcs.anl.gov>:
>
>> billy at dem.uminho.pt writes:
>>
>>   Its definitely possible. Usually you need to know something about
>> your system in order to precondition and solve it effectively. For
>> instance,
>> is it the discretization of an elliptic operator?
>>
>>    Matt
>>
>> > Hi,
>> >
>> >
>> > I have been testing my parallel implementation with a 2D case. I have used
>> the
>> > following grids with 2 and 4 processes: 4x4, 10x10, 16x16 and 18x18.
>> >
>> > It works for the first three (max. number of iterations to converge aprox.
>> 70)
>> > but when I increase to 18x18 the matrix does not converge. I have increased
>> the
>> > maximum number of iterations and I have used GMRES, BiCGSTAB with
>> > preconditioners ASM, JACOBI, etc.
>> >
>> > With KSPType = GMRES and PCType = ASM:
>> > Number of iterations: 500 Residual: +1.420471E-01
>> >
>> > With KSPType = GMRES and PCType = JACOBI:
>> > Number of iterations: 500 Residual: +2.351882E-02
>> >
>> > With KSPType = BCGS and PCType = ASM:
>> > Number of iterations: 136 Residual: +3.911446E+04
>> >
>> > With KSPType = BCGS and PCType = NULL:
>> > Number of iterations: 157 Residual: +3.254728E+03
>> >
>> > Is it normal that the convergence detiorates so much with such a slight
>> increase
>> > in the dimension of the matrix? Is there any optimization parameter that I
>> may
>> > be missing?
>> >
>> >
>> > Billy.
>> >
>> >
>> >
>>
>> --
>> "Failure has a thousand explanations. Success doesn't need one" -- Sir Alec
>> Guiness
>>
>>
>
>
>
>

--
"Failure has a thousand explanations. Success doesn't need one" -- Sir Alec Guiness

```