• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.205-212
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• 2007

Parabolic approximation wave models based on $Pad{\acute{e}}$ approximants are analyzed in order to calculate wave transformation. In this study a $Pad{\acute{e}}(2,2)$ parabolic approximation model is developed to increase the accuracy of computation in comparison with the existing models. Numerical studies on a constant sloping bed show that the new model proves to allow for much more successful treatment of large angles of incidence than is possible using the previously available models.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.4
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• pp.375-384
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• 2007

Parabolic approximation wave models based on $Pad{\acute{e}}$ approximants are presented of which the $Pad{\acute{e}}$(15, 15) is shown to be applicable to incidence angle $80^{\circ}$ in comparison with the exact solution of a constant sloping bed. After introducing a systematic way of the derivation to the parabolic wave equation, parabolic models are obtained in this study upto the 15th order and several numerical results are given to wave transformation in a constant sloping bed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.279-284
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• 2011

The calculation of Zwicker's loudness which is needed for multiple frequency response with a fine frequency resolution using the finite element (FE) procedure usually requires significant computation time since a numerical solution must be obtained for each considered frequency. Furthermore, if the analysis is the basis for an iterative optimization procedure this approach imposes high computational cost. In this work, we present an efficient approach for obtaining Zwicker's loudness via the Pad$\acute{e}$ approximants and applying in an acoustical topology optimization procedure. The paper is focused on an efficient and accurate calculation of Zwicker's loudness, design sensitivity analysis, and the acoustical topology optimization method by using Pad$\acute{e}$ approximants. The paper compares the efficient algorithm to results obtained by a standard FEM. Comparison are made both in terms of accuracy and in terms of CPU-times needed for the calculation.

• The Journal of the Acoustical Society of Korea
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• v.25 no.5
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• pp.229-238
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• 2006

This paper shows the analytic error caused by the inconsistency of the approximation order between the non local boundary condition (NLBC) and the parabolic governing equation. To obtain the analytic error, we first transform the NLBC to the half space domain using plane wave analysis. Then, the analytic error is derived on the boundary between the true numerical domain and the half space domain equivalent to the NLBC. The derived analytic error is physically expressed as the artificial reflection. We examine the characteristic of the analytic error for the grazing angle, the approximation order of the PE or the NLBC. Our main contribution is to present the analytic method of error estimation and the application limit for the high order parabolic equation and the NLBC.

• Ocean Systems Engineering
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• v.6 no.1
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• pp.117-128
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• 2016

A theoretical study of Boussinesq equations (BEs) for internal waves propagating in a two-fluid system is presented in this paper. The two-fluid system is assumed to be bounded by two rigid plates. A set of three equations is firstly derived which has three main unknowns, the interfacial displacement and two velocity potentials at arbitrary elevations for upper and lower fluids, respectively. The determination of the optimal BEs requires a solution of depth parameters which can be uniquely solved by applying the $Pad{\acute{e}}$ approximation to dispersion relation. Some wave properties predicted by the optimal BEs are examined. The optimal model not only increases the applicable range of traditional BEs but also provides a novel aspect of internal wave studies.