National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 18 Jun 2024 05:54:41 GMT2024-06-18T05:54:41Z5041Indirect boundary element method combining extra fundamental solutions for solving exterior acoustic problems with fictitious frequencieshttp://scholars.ntou.edu.tw/handle/123456789/2494Title: Indirect boundary element method combining extra fundamental solutions for solving exterior acoustic problems with fictitious frequencies
Authors: Jia-Wei Lee; Jeng-Tzong Chen; Chi-Feng Nien
Abstract: The authors propose an alternative approach to solve the problem of fictitious frequencies. It is different from the mixed potential approach in the indirect method as well as the Burton and Miller approach in the direct boundary element method (BEM). The authors add some fundamental solutions with unknown strength in the solution representation to complete the solution space. From the viewpoint of the adding source, the present idea is similar to the combined Helmholtz interior integral equation formulation (CHIEF) method. The difference between the added source point and null-field point of CHIEF is their role. The former supplies the deficient basis due to the fictitious frequency while the latter provides the extra constraint equation. It can be alternatively found by adding the right unitary vectors of zero singular value. The bordered matrix is invertible for the fictitious frequency if the extra source points do not locate at the failure position. This is the reason why the property is analogous to the CHIEF method in the direct BEM. Therefore, it can fill in the blank area of why there is no CHIEF method in the indirect method. The authors also analytically derive the locations of possible failure source points by using the degenerate kernel.
Wed, 29 May 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/24942019-05-29T00:00:00ZComputation of scattering of a plane wave from multiple prolate spheroids using the collocation multipole methodhttp://scholars.ntou.edu.tw/handle/123456789/2507Title: Computation of scattering of a plane wave from multiple prolate spheroids using the collocation multipole method
Authors: Lee, W. M.; Jeng-Tzong Chen
Abstract: The collocation multipole method is presented to solve three-dimensional acoustic scattering problems with multiple prolate spheroids subjected to a plane sound wave. To satisfy the three-dimensional Helmholtz equation in prolate spheroidal coordinates and the radiation condition at infinity, the scattered field is formulated in terms of radial and angular prolate spheroidal wave functions. Instead of using the complicated addition theorem of prolate spheroidal wave functions, the multipole method, the directional derivative, and the collocation technique are combined to solve multiple scattering problems semi-analytically. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure with respect to a non-local prolate spheroidal coordinate system is developed without any truncation error for multiply connected domain problems. By truncating the higher order terms of the multipole expansion, a finite linear algebraic system is obtained and the scattered field is determined from the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure and the far field scattering pattern are determined. Numerical experiments for convergence are performed to provide the guide lines for the proposed method. The proposed results of acoustic scattering by one, two, and three prolate spheroids are compared with those of an available analytical method and the boundary element method to validate the proposed method. Finally, the effects of the eccentricity of a prolate spheroidal scatterer, the separation between scatterers and the incident wave number on the near-field acoustic pressure and the far-field scattering pattern are investigated.
Mon, 03 Oct 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/25072016-10-03T00:00:00ZComment on "Eigenmode analysis of arbitrarily shaped two-dimensional cavities by the method of point matching" [J. Acoust. Soc. Am. 107, 1153 (2000)]http://scholars.ntou.edu.tw/handle/123456789/2337Title: Comment on "Eigenmode analysis of arbitrarily shaped two-dimensional cavities by the method of point matching" [J. Acoust. Soc. Am. 107, 1153 (2000)]
Authors: Jeng-Tzong Chen; Chang, M. H.; Chung, I. L.; Cheng, Y. C.
Abstract: The method of point matching proposed by Kang and Lee [J. Acoust. Soc. Am. 107, 1153–1160 (2000)] is revisited. This method can be seen as a single-layer potential approach from the viewpoint of imaginary-part dual BEM developed by Chen et al. [J. Chin. Inst. Eng. 12, 729–739 (1999)]. Based on the concept of double-layer potential, an innovative method is proposed to deal with the problem of spurious eigensolution for the Neumann problem. Also, the acoustic mode is analytically derived for the circular cavity. Both the analytical study for a circular case and numerical result for a square cavity show the validity of the proposed formulation.
Thu, 17 Jan 2002 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23372002-01-17T00:00:00ZA new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation methodhttp://scholars.ntou.edu.tw/handle/123456789/2328Title: A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method
Authors: Chen, I. L.; Jeng-Tzong Chen; Kuo, S. R.; Liang, M. T.
Abstract: Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.
Thu, 01 Mar 2001 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23282001-03-01T00:00:00Z