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Keywords: optical waves, high oscillations, ray transformation, finite differences, decomposition method, mesh adaptation.

Summary

Various types of decomposed finite difference methods possess extraordinary features such as structure simplicity, computational efficiency and remarkable flexibility in applications. Naturally, decomposition methods with adaptations lead to fascinating approaches to computation, and ensure effective strategies in simulation realizations. This paper proposes an exponential transformation which removes successfully the transverse-wise high oscillation component from the complex solution of Helmholtz equation for alternating direction implicit operations. Arclength adaptation is introduced in the wave propaganda direction. The idea is to take advantage of the known ray approximation for the optical wave function. Coupled nonoscillatory ray equations are obtained for continuing splitting approximations. Hence, the ray transformation and decomposition successfully remove the oscillatory factor for successive simulations. The straightforward procedure is remarkable for fast calculations without utilizing tiny mesh step sizes.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 105 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 53 Adaptive Decomposition Methods for the Solution of Certain Highly Oscillatory Optical Wave Problems Q. Sheng Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, United States of America doi:10.4203/ccp.105.53 purchase the full-text of this paper Full Bibliographic Reference for this paper Q. Sheng, "Adaptive Decomposition Methods for the Solution of Certain Highly Oscillatory Optical Wave Problems", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 53, 2014. doi:10.4203/ccp.105.53 Keywords: optical waves, high oscillations, ray transformation, finite differences, decomposition method, mesh adaptation. Summary Various types of decomposed finite difference methods possess extraordinary features such as structure simplicity, computational efficiency and remarkable flexibility in applications. Naturally, decomposition methods with adaptations lead to fascinating approaches to computation, and ensure effective strategies in simulation realizations. This paper proposes an exponential transformation which removes successfully the transverse-wise high oscillation component from the complex solution of Helmholtz equation for alternating direction implicit operations. Arclength adaptation is introduced in the wave propaganda direction. The idea is to take advantage of the known ray approximation for the optical wave function. Coupled nonoscillatory ray equations are obtained for continuing splitting approximations. Hence, the ray transformation and decomposition successfully remove the oscillatory factor for successive simulations. The straightforward procedure is remarkable for fast calculations without utilizing tiny mesh step sizes. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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