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

[Mark F. Adams]

On Nov 11, 2011, at 11:20 AM, Jed Brown wrote:

> 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?

Jed, I agreed with this point in my email.  And I can now see your point that using the preconditioned residual is a good default for PETSc, or at least I'm willing to defer to your judgment.

> 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.

All I recall was that I was confused because the residual dropped 10 orders of magnitude, apparently, in the first iteration and Barry explained the issue, I added 'unpreconditioned' residual and it was fine.  So if I am recalling this correctly this default confused me but apparently, or what I infer from this discussion, more users get confused with using the unpreconditioned residual so you've chosen preconditioned residual as the default.

Mark

>  
> 
> 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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