[petsc-users] Multigrid preconditioner parameters

[Feng Xing]

In detail, the equation is div( K(x) grad(u) ) = f, where K(x) could be a variable coefficient or a constant, in a nice domain ((0,1)^3). The problem is defined on a nice domain like (0,1)^3. Laplace is a special case if K(x)=cst. So I wanted to try to understand it (convergence of multigrid ). 

Regards,

> On 29 May 2015, at 21:55, Jed Brown <jed at jedbrown.org> wrote:
> 
> Feng Xing <snakexf at gmail.com> writes:
>> It’s a variation of 3d Poisson equation ( -Delta u=f, u is unknown, f
>> is a given function ). Mathematically, they have similar properties.
> 
> Variable coefficients?  Negative shift?  Geometry?  (These totally
> change the behavior of the equation.)  Or really just a Laplacian in a
> nice domain?
> 
>> So, I didn’t precise the details to make it look like too
>> complicated. Numerically, the discretisation is by the standard finite
>> element method or the finite volume method.
> 
> So this is a test problem and nobody cares about the answer?  You're
> using it as a proxy for something else?
> 
> It is extremely common to reach misleading conclusions when using the
> Laplacian as a test.  If you really care about solving this particular
> problem efficiently, there are a myriad of techniques for improving
> performance by orders of magnitude.
> myriad