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 <[email protected]> wrote: > > Feng Xing <[email protected]> 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
