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From: Michael L. H. <Ha...@la...> - 2003-08-12 16:27:02
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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
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