[petsc-dev] [petsc-users] Any suggestion for this kinds of matrix?

[Jed Brown]

On Fri, Nov 11, 2011 at 10:08, Mark F. Adams <mark.adams at columbia.edu>wrote:

> First, "my" matrices (actually XGC1 matrices from one of my projects and I
> don't even know exactly what they do) put 1.0 on the diagonal for BCs and
> god knows how the thing is scaled (1e13 apparently).  But this does not
> matter because the RHS and initial guess are 0.0 so the BCs have been
> completely removed from the algebra, even if they are still in the data
> structures.
>

So what happens when you use the same method with inhomogeneous Dirichlet
conditions? This is especially bad if the interior is scaled by, say, 1e-13
instead of 1e+13, because the boundary conditions dominate the initial
residual.


>
> As I recall the preconditioned residual was confusing because since these
> are Laplacian matrices with a scale of 1e13, as you found, the residual
> dropped like 10 orders of magnitude in the first iteration, which was
>  pretty confusing.
>

The preconditioned residual fixes the scaling. If you evaluate the initial
unpreconditioned residual, then you see the confusing scaling. But
preconditioning, even with just Jacobi, fixes the scaling.


>
> So I don't see these XGC1 problems as being arguments for preconditioned
> residual, in fact they argue against it, right?
>

The preconditioned residual fixes the scaling, assuming it is no worse than
Jacobi.
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