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An approximately H-1-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography

Pimprikar, N and Teresa, J and Roy, D and Vasu, RM and Rajan, K (2013) An approximately H-1-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography. In: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 92 (1). pp. 33-61.

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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 H-1 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.

Item Type: Journal Article
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Additional Information: Copyright of this article is belongs to TECH SCIENCE PRESS
Keywords: H-1 optimality; meshfree methods; Helmholtz equation; numerical pollution; optical tomography
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Division of Physical & Mathematical Sciences > Instrumentation and Applied Physics (Formally ISU)
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 02 Oct 2013 06:09
Last Modified: 02 Oct 2013 06:09
URI: http://eprints.iisc.ernet.in/id/eprint/47370

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