Open Access

ARTICLE

An approximately H¹-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography

by N Pimprikar¹, J Teresa², D Roy¹, R M Vasu⁴, K Rajan⁴

1 Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India
2 Department of Physics, Indian Institute of Science, Bangalore 560012, India
3 Communicating author; Email: royd@civil.iisc.ernet.in
4 Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India

Computer Modeling in Engineering & Sciences 2013, 92(1), 33-61. https://doi.org/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 weak form of any jump boundary terms. For numerical demonstration of the above formulation, we used a multimode optical fiber in an index matching liquid as the object. The scattered intensity and its normal derivative are computed from the scattered field obtained by solving the Helmholtz equation, using the new formulation and the conventional finite element method. By comparing the results with the experimentally measured scattered intensity, the stability of the solution through the new formulation is demonstrated and its closeness to the experimental measurements verified.

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