Re: [Chama-developers] convergence problems

[Michael L. H. <Ha...@la...>]

Austin Minnich writes:
> in particular, it seems to be the alpha choice of LSLR that is not 
> converging....something's funny with that one.

Yes, it is different. How, you say?

Well, for a constant D, the choices for harmonic average D simplify
a bit. Choices beta, gamma and delta all reduce to the constant
D value, regardless of the geometry (look at the definitions and
assume D1=D2=D). So, in other words, beta, gamma and delta LSLR are
all equivalent for constant D problems. In fact, we can skip running
two of them on all the constant D problems (1-5).

Choice alpha, however, does not simplify to D for constant D. It
simplifies to:
                        |\vec{r}_1 - \vec{r}_2|
  D_{12}^h = D ---------------------------------------------
               |\vec{\Delta r}_{1f}| + |\vec{\Delta r}_{2f}| 

On an orthogonal mesh with constant D, this does simplify to D. But
for a general mesh, it doesn't. Choice alpha has some other good
properties, mainly in conjunction with choices for DeltaR in the
Skewed-Ortho methods. But it doesn't seem to be good for LSLR on
constant D problems...

-Mike