# Matrix convergence.

billy at dem.uminho.pt billy at dem.uminho.pt
Thu Mar 2 16:31:29 CST 2006

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Yes, it is non-symmetric. Should I optimize the renumbering of the cells to
someway reduce the bandwidth of the matrix?

Billy.

Quoting Matthew Knepley <knepley at mcs.anl.gov>:

> 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
>
>

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