scholarly journals Coupled Mode Sound Propagation in Inhomogeneous Stratified Waveguides

2021 ◽  
Vol 11 (9) ◽  
pp. 3957
Author(s):  
Juan Liu ◽  
Qi Li
Keyword(s):  
Differential Equations ◽  
Sound Propagation ◽  
Computational Cost ◽  
Acoustic Medium ◽  
Acoustic Fields ◽  
Local Modes ◽  
Finite Element Software ◽  
Coupled Mode ◽  
Mode Method ◽  
Admittance Method

An efficient coupled mode method for modeling sound propagation in horizontally stratified inhomogeneous waveguides, in which the seabed is modeled as a (layered) acoustic medium, is presented. The method is based on Fawcett’s coupled mode method and the multimodal admittance method. The acoustic field is expanded onto the unusual local eigenfunctions composed by normal modes in the corresponding one-layer homogeneous waveguides with constant depth equal to the local total depth of the multilayered waveguide. A set of energy-conserving first-order differential equations governing the modal amplitudes of acoustic fields is derived. The admittance method is employed to solve the differential equations in a numerically stable manna. The coupled mode method considers the backscattering effect of inhomogeneities and full coupling between local modes, and offers improvement from the viewpoint of efficiency and computational cost. The acoustic fields predicted by the method agree well with those computed by the commercial finite element software COMSOL Multiphysics. The method can be extended to further establish fast and accurate 3D sound propagation models in complex shallow water environments.

scholarly journals A coupled-mode method for sound propagation with multiple sources in range-dependent waveguides

2015 ◽  
Vol 45 (1) ◽  
pp. 014301-014301
Author(s):  
WenYu LUO ◽  
RenHe ZHANG ◽  
JiXing QIN ◽  
ChunMei YANG
Keyword(s):  
Sound Propagation ◽  
Multiple Sources ◽  
Coupled Mode ◽  
Mode Method

scholarly journals A coupled-mode method for sound propagation in a range-dependent penetrable waveguide

2013 ◽  
Vol 62 (9) ◽  
pp. 094302
Author(s):  
Yang Chun-Mei ◽  
Luo Wen-Yu ◽  
Zhang Ren-He ◽  
Qin Ji-Xing
Keyword(s):  
Sound Propagation ◽  
Coupled Mode ◽  
Mode Method

COUPLED MODE AND FINITE ELEMENT APPROXIMATIONS OF UNDERWATER SOUND PROPAGATION PROBLEMS IN GENERAL STRATIFIED ENVIRONMENTS

2008 ◽  
Vol 16 (01) ◽  
pp. 83-116 ◽  
Author(s):  
G. A. ATHANASSOULIS ◽  
K. A. BELIBASSAKIS ◽  
D. A. MITSOUDIS ◽  
N. A. KAMPANIS ◽  
V. A. DOUGALIS
Keyword(s):  
Finite Element ◽  
Sound Propagation ◽  
Test Problems ◽  
Underwater Sound ◽  
Finite Element Approximations ◽  
Coupled Mode ◽  
Cylindrically Symmetric ◽  
Mode Method ◽  
Acoustic Waveguides ◽  
Good Agreement

We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms.

scholarly journals A coupled-mode method for sound propagation in range-dependent waveguides

2021 ◽  
Vol 70 (6) ◽  
pp. 064301-064301
Author(s):  
Liu Juan ◽  
◽  
Li Qi ◽  
◽  
Keyword(s):  
Sound Propagation ◽  
Coupled Mode ◽  
Mode Method

Multilevel Monte Carlo by using the Halton sequence

2020 ◽  
Vol 26 (3) ◽  
pp. 193-203
Author(s):  
Shady Ahmed Nagy ◽  
Mohamed A. El-Beltagy ◽  
Mohamed Wafa
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Random Numbers ◽  
Multilevel Monte Carlo ◽  
Halton Sequence ◽  
Random Generator ◽  
Mc Simulation ◽  
Multilevel Monte Carlo Method

AbstractMonte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

CLASSIFICATION OF BUCKLING MODES IN STIFFENED FUNCTIONALLY GRADED COMPOSITE TUBES SUBJECT TO BENDING

2021 ◽  
Author(s):  
LUAN TRINH ◽  
PAUL WEAVER
Keyword(s):  
Wall Thickness ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Mode Shapes ◽  
Local Mode ◽  
Buckling Mode ◽  
Global Mode ◽  
Local Modes ◽  
Linear Discriminant ◽  
Finite Element Software

Bamboo poles, and other one-dimensional thin-walled structures are usually loaded under compression, which may also be subject to bending arising from eccentric loading. Many of these structures contain diaphragms or circumferential stiffeners to prevent cross-sectional distortions and so enhance overall load-carrying response. Such hierarchical structures can compartmentalize buckling to local regions in addition to withstanding global buckling phenomena. Predicting the buckling mode shapes of such structures for a range of geometric parameters is challenging due to the interaction of these global and local modes. Abaqus finite element software is used to model thousands of circular hollow tubes with random geometric parameters such that the ratios of radius to periodic length range from 1/3-1/7, the ratio of wall thickness to radius varies from 1/4-1/10. The material used in this study is a type of bamboo, where the Young’s and shear moduli are point-wise orthotropic and gradually increase in magnitude in the radial direction. Under eccentric loads with varying eccentricity, the structures can buckle into a global mode or local modes within an internode, i.e. periodic unit. Moreover, the local modes may contain only one wave or multiple waves in the circumferential direction. As expected, numerical results show that the global mode is more likely to occur in small and thick tubes, whereas the local modes are observed in larger tubes with a smaller number of circumferential waves present in thicker walls. Also, greater eccentricity pushes the local mode domains towards smaller tubes. An efficient classification method is developed herein to identify the domains of each mode shape in terms of radius, wall thickness and eccentricity. Based on linear discriminant analysis, explicit boundary surfaces for the three domains are defined for the obtained data, which can help designers in predicting the mode shapes of tubular structures under axial bending.

scholarly journals CMMSE: A technique for generating adapted discretizations to solve partial differential equations with the generalized finite difference method

2021 ◽  
Author(s):  
Augusto César Ferreira ◽  
Miguel Ureña ◽  
HIGINIO RAMOS
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Meshless Method ◽  
Computational Cost ◽  
Partial Differential

The generalized finite difference method is a meshless method for solving partial differential equations that allows arbitrary discretizations of points. Typically, the discretizations have the same density of points in the domain. We propose a technique to get adapted discretizations for the solution of partial differential equations. This strategy allows using a smaller number of points and a lower computational cost to achieve the same accuracy that would be obtained with a regular discretization.

scholarly journals Higher Order Haar Wavelet Method for Solving Differential Equations

2020 ◽  
Author(s):  
Jüri Majak ◽  
Mart Ratas ◽  
Kristo Karjust ◽  
Boris Shvartsman
Keyword(s):  
Differential Equations ◽  
Computational Cost ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Convergence Results ◽  
Key Characteristics ◽  
Parameter Values ◽  
Excellent Accuracy

The study is focused on the development, adaption and evaluation of the higher order Haar wavelet method (HOHWM) for solving differential equations. Accuracy and computational complexity are two measurable key characteristics of any numerical method. The HOHWM introduced recently by authors as an improvement of the widely used Haar wavelet method (HWM) has shown excellent accuracy and convergence results in the case of all model problems studied. The practical value of the proposed HOHWM approach is that it allows reduction of the computational cost by several magnitudes as compared to HWM, depending on the mesh and the method parameter values used.

Efficient Modal Analysis of Bianisotropic Waveguides by the Coupled Mode Method

2007 ◽  
Vol 55 (1) ◽  
pp. 108-116 ◽  
Author(s):  
Jaime Pitarch ◽  
Jos M. Catala-Civera ◽  
Felipe L. Penaranda-Foix ◽  
Miguel A. Solano
Keyword(s):  
Modal Analysis ◽  
Coupled Mode ◽  
Mode Method

scholarly journals High Accuracy Combination Method for Solving the Systems of Nonlinear Volterra Integral and Integro-Differential Equations with Weakly Singular Kernels of the Second Kind

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Lu Pan ◽  
Xiaoming He ◽  
Tao Lü
Keyword(s):  
Differential Equations ◽  
Computational Cost ◽  
Posteriori Error ◽  
High Accuracy ◽  
Combination Method ◽  
Weakly Singular Kernels ◽  
A Posteriori Error ◽  
Weakly Singular ◽  
Accuracy Order ◽  
Singular Kernels

This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover an a posteriori error estimation for the algorithm is derived. Both of the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational cost.

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