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hbzhang / mpspack

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Kress-style reparametrization of segments to handle corners #28

Closed GoogleCodeExporter closed 8 years ago

GoogleCodeExporter commented 8 years ago 
Test it on triangle eigenvalues, and square scattering.

Ultimately will be replaced by a compressed corner rep from fast direct solver?

Original issue reported on code.google.com by alex.h.b...@gmail.com on 21 Dec 2011 at 4:41

GoogleCodeExporter commented 8 years ago 
As of r170 this is done, using Kress 1991 graded power-law scheme. 
Interior/Exterior Helmholtz BVPs are tested with test/testcornerquad.m and its 
various choices.
Non-reentrant corners get 1e-14 with q=4 best. Reentrant corners get only 1e-6, 
with q=7 best, and slow 3rd-order convergence. The limitations now are:
* NaN failure mode when s(1).x(end) and s(2).x(1) are < e_mach apart (as with 
Adrianna). This occurs for higher q (>5) with N only 150 or so.
* exponential (sinh-based?) grading would be better, since points get too far 
apart.

One question is why the density only blows up *very* close to corner, ie 1e-10. 
There doesn't seem to be any cause at this lengthscale, and cond(A)=1e5 only.

Anyway, example/tridrummodes.m demos this in a triangle.

Original comment by alex.h.b...@gmail.com on 16 Jan 2012 at 6:42