Sung-Shan Hsiao

Solutions of boundary detection problem for modified Helmholtz equation by Trefftz method

The boundary detection problem, which is governed by modified Helmholtz equation, is analysed by the Trefftz method and the exponentially convergent scalar homotopy algorithm (ECSHA). The spatial position for part of boundary with given boundary condition is unknown; therefore, it is very difficult to analyse the boundary detection problem by any numerical scheme. In this study, we used the Trefftz method to analyse the boundary detection problem, governed by the modified Helmholtz equation, and the numerical solution of Trefftz method is expressed as a linear combination of the T-complete functions. By using the Trefftz method to analyse the problem, a system of non-linear algebraic equations will be formed and then solved by the ECSHA which will converge exponentially. The unknown coefficients in Trefftz method and the spatial position of the unknown boundary positions can be simultaneously found via evolutionary process of the ECSHA. Some numerical examples will be provided to validate the accuracy and efficacy of the proposed scheme.

A drbem model for harbor oscillation with the effect of energy dissipation

Abstract In this study, the numerical scheme of dual reciprocity boundary element method (DRBEM) is adopted to investigate the resonant problem in a harbor while considering the effect of energy dissipation. The numerical model employed the mild slope equation as a basic equation. To avoid complicated procedures for solving the equation, DRBEM is used to improve numerical efficiency. Computation results are compared with the existing experimental data and other theoretical results. It shows that the present model is valid and effective to solve the harbor oscillation problem.

WAVE TRANSFORMATION OVER AN ELLIPTIC SHOAL ON A SLOPING BOTTOM

This study investigates wave transformations over an elliptic shoal on a sloping bottom using numerical calculations. The theoretical model is based on the fully nonlinear Boussinesq equation that was applied by Chen et al. [2003]. This equation is expressed by the velocity at any level below the surface. The momentum equation is derived using modified vertical vorticity terms from the equation by Wei et al. [1995]. Bottom friction, wave breaking, and subgrid lateral turbulent mixing proposed by Kennedy et al. [2000] are also included in the equations. Several numerical experiments are conducted for waves with incident angles of 0°, 15°, and 30°. The numerical results demonstrate the phenomena of wave focusing in the rear of the elliptic shoal. The wave focusing not only results in a smaller wave-induced current on top of the shoal than that at the rear of the shoal, but also a strong return flow at the back of the shoal. It. is found that the non-dimensional wave height in the wave-focusing zone increases as the relative water depth decreases. Moreover, the orientation of wave height contours in the focusing region is almost identical to that of the incident wave angle. This phenomenon stays true for different incident wave periods.

The Kriging Cloud Computing Framework: Interpolation of Topography by Cloud Computing with the Kriging Algorithm

Spatial information surveyed by photogrammetry, airborne LiDAR and Mobile Measurement System (MMS) above ground level can be analyzed by scientists using standard geostatistical methodologies such as ordinary Kriging and sequential Gaussian simulation to interpolate heterogeneities of profiles from sparse sample data. Proven effective by researchers, the Kriging algorithm model is used by commercial data analysis packages for instant interpolation. However, meaningful and reliable results only come with a comprehensive understanding of the variogram associated with valid mathematical functions. To capture spatial landscape variations from massive sample grids of satellite images, this paper presents a cloud computing-based automation approach to improve topography interpolation by taking advantage of rapid computation speed through an open-source cross platform to enrich internet applications. The research team conducted a pilot test on sand beaches, developed the Kriging Cloud Computing Framework, streamlined the Kriging algorithm, developed Kriging Variogram Data Bank and Parameter Management System, derived cross validation procedures and built in Application Programming Interface, API. This new technology can benefit end users around the world in acquiring of ground profiles and production of Digital Elevation Models (DEMs) while requiring only minimal knowledge of the Kriging Method. This cloud computing system facilitates user data input, parameter selection, fast data analysis and model output. The application of this new framework improves remote sensing technology and GIS applications in a variety of unreachable terrains, such as deserts, swamps, and dense forests.

The Least Squares Trefftz Method and the Method of External Source for the Eigenfrequencies of Waveguides

In this study, the least squares Trefftz method (LSTM) is adopted for analyzing the eigenfrequencies problems governed by homogeneous Helmholtz equations. The Trefftz method, one kind of boundary-type meshless collocation methods, does not need mesh generation and numerical quadrature. Since the system of linear algebraic equations obtained by Trefftz method is highly ill-conditioned, the least squares method is adopted to stabilize the numerical scheme in this study. In the eigenproblem, the response amplitudes from an external source are used to determine the resonant frequencies. By adding an external source, the homogeneous boundary condition becomes inhomogeneous. Then we can employ the LSTM to easily solve this problem. In this paper, the LSTM and the method of external source are used to solve this eigenfrequencies problems governed by Helmholtz equations. Several numerical examples are provided to verify the accuracy and the simplicity of the proposed numerical scheme.

Prediction of Typhoon Swells Using Neural Networks

A back-propagation neural network was employed to predict swells generated by typhoons, which damages of property and take human life in nearshore areas. Fifteen sets of records of wave-heights during typhoons around the east coast of Taiwan were used to develop and validate the network. The current and previous values of the maximum speed of the wind storms, W(subscript max); the speed of the typhoon, V; the distance from the center of typhoon to the observing station, d; the radius of force 7 wind, R7; the azimuthal angle, θ1 measured clockwise from north to the direction of motion, and the angle between the direction of motion of the typhoon and the line that connects the center of the typhoon to the observing station, θ2; and the significant wave heights recorded at the stations, H(subscript b), were used as input parameters. The predicted significant wave heights, H(subscript p), were selected as the output parameters. The network predicts the maximum significant wave heights quite effectively and the differences between the predicted and measured maximum wave heights are less than 13.5 % of the maximum measured wave heights. All the evidence shows that the developed Back-Propagation Neural Network is an effective method for predicting a swell.