N Pimprikar1, J Teresa2, D Roy1,3, R M Vasu4, K Rajan4
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 33-61, 2013, DOI:10.3970/cmes.2013.092.033
Abstract Nearly pollution-free solutions of the Helmholtz equation for k-values corresponding to visible light are demonstrated and verified through experimentally measured forward scattered intensity from an optical fiber. Numerically accurate solutions are, in particular, obtained through a novel reformulation of the H1 optimal Petrov-Galerkin weak form of the Helmholtz equation. Specifically, within a globally smooth polynomial reproducing framework, the compact and smooth test functions are so designed that their normal derivatives are zero everywhere on the local boundaries of their compact supports. This circumvents the need for a priori knowledge of the true solution on the support boundary and relieves the… More >
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