scholarly journals Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Large Scale ◽  
Boundary Integral ◽  
Practical Significance ◽  
Fast Multipole ◽  
Tree Structures ◽  
Wave Problems ◽  
Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

Fast Multipole Boundary Element Method for 3-D Full- and Half-Space Acoustic Wave Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Large Scale ◽  
Fast Multipole ◽  
Wave Problems ◽  
Acoustic Bem ◽  
Element Method

In this paper, the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 3-D full- and half-space domains will be discussed. First, the fast multipole BEM formulations will be presented and then improvements to the formulations and algorithms will be discussed. Examples with large-scale acoustic BEM models, with the DOFs above 2 millions and solved on desktop PCs, will be presented to demonstrate the potential of the fast multipole BEM for modeling large-scale structural acoustic problems.

The Mixed Fast Multipole Boundary Element Method for Solving Strip Cold Rolling Process

2010 ◽  
Vol 20-23 ◽  
pp. 76-81 ◽  
Author(s):  
Hai Lian Gui ◽  
Qing Xue Huang
Keyword(s):  
Variational Inequality ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Mixed Boundary ◽  
Contact Problems ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Mixed Variational Inequality ◽  
Element Method

Based on fast multipole boundary element method (FM-BEM) and mixed variational inequality, a new numerical method named mixed fast multipole boundary element method (MFM-BEM) was presented in this paper for solving three-dimensional elastic-plastic contact problems. Mixed boundary integral equation (MBIE) was the foundation of MFM-BEM and obtained by mixed variational inequality. In order to adapt the requirement of fast multipole method (FMM), Taylor series expansion was used in discrete MBIE. In MFM-BEM the calculation time was significant decreased, the calculation accuracy and continuity was also improved. These merits of MFM-BEM were demonstrated in numerical examples. MFM-BEM has broad application prospects and will take an important role in solving large-scale engineering problems.

Numerical Simulations of Large Deep Water Waves: The Application of a Boundary Element Method

2006 ◽  
Author(s):  
Caroline H. Hague ◽  
Chris Swan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Deep Water ◽  
Water Waves ◽  
Physical Space ◽  
Wave Model ◽  
Three Dimensions ◽  
Fully Nonlinear ◽  
Highly Nonlinear ◽  
Element Method

This paper concerns the description of extreme surface water waves in deep water. A fully nonlinear numerical wave model in three dimensions is presented, based on the Boundary Element Method (BEM), and is applied to nonlinear focusing of wave components with varying frequency and direction of propagation to form highly nonlinear groups. By using multiple fluxes at corners and edges of the numerical domain the “corner problem” associated with BEM-based models in physical space is overcome. A two-dimensional version of the method is also employed to model unidirectional cases, and examples presented include the focusing of Top Hat spectra in deep water to form highly nonlinear wave groups at or close to their breaking limit. The ability of the model to accurately simulate these sea states is highlighted by comparison to the fully nonlinear model of Bateman, Swan and Taylor (2001, 2003).

Study on Numerical Methods for Acoustic Radiation of Open Structure

2010 ◽  
Vol 439-440 ◽  
pp. 692-697
Author(s):  
Li Jun Li ◽  
Xian Yue Gang ◽  
Hong Yan Li ◽  
Shan Chai ◽  
Ying Zi Xu
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Coupling Method ◽  
Open Structure ◽  
Acoustic Coupling ◽  
Infinite Element Method ◽  
Direct Boundary Element Method ◽  
Element Method

For acoustic radiation of open thin-walled structure, it was difficult to analyze directly by analytical method. The problem could be solved by several numerical methods. This paper had studied the basic theory of the numerical methods as FEM (Finite Element Method), BEM (Boundary Element Method) and IFEM (Infinite Element Method), and the numerical methods to solve open structure radiation problem. Under the premise of structure-acoustic coupling, this paper analyzed the theory and flow of the methods on acoustic radiation of open structure, including IBEM (Indirect Boundary Element Method), DBEM (Direct Boundary Element Method) coupling method of interior field and exterior field, FEM and BEM coupling method, FEM and IFEM coupling method. This paper took the open structure as practical example, and applied the several methods to analyze it, and analyzed and compared the several results to get relevant conclusions.

Application Incompatible Element in Mixed Fast Multipole Boundary Element Method

2010 ◽  
Vol 439-440 ◽  
pp. 80-85
Author(s):  
Hai Lian Gui ◽  
Qing Xue Huang ◽  
Ya Qin Tian ◽  
Zhi Bing Chu
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Fast Multipole ◽  
Mixed Variational Inequality ◽  
Calculation Time ◽  
Incompatible Elements ◽  
Improve Calculation ◽  
Compatible Elements ◽  
Element Method

Based on fast multipole boundary element method (FM-BEM) and mixed variational inequality, a new method named mixed fast multipole boundary element method (MFM-BEM) was presented in this paper. In order to improve calculation time and accuracy, incompatible elements as interpolation functions were used in the algorithm. Elements were optimized by mixed incompatible elements and compatible elements. On the one hand, the difficult to satisfy precise coordinate was avoided which caused by compatible elements; on the other hand, the merits of MFM-BEM were retained. Through analysis of example, it was conclusion that calculation time and accuracy were improved by MFM-BEM, calculation continuity was also better than traditional FM-BEM. With increasing of degree of freedom, calculation time of MFM-BEM grew slower than the time of traditional FM-BEM. So MFM-BEM provided a theoretical basis for solving large-scale engineering problems.

scholarly journals The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method

2011 ◽  
Vol 18 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Hassan Ghassemi ◽  
Ehsan Yari
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Boundary Element ◽  
Mass Matrix ◽  
Added Mass ◽  
Experimental Results ◽  
Marine Propellers ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Element Method

The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method Added mass is an important and effective dynamic coefficient in accelerating, non uniform motion as a result of fluid accelerating around a body. It plays an important role, especially in vessel roll motion, control parameters as well as in analyzing the local and global vibration of a vessel and its parts like propellers and rudders. In this article, calculating the Added Mass Coefficient has been examined for a sphere, ellipsoid, marine propeller and hydrofoil; using numerical Boundary Element Method. Since an Ellipsoid and a sphere have simple geometric shapes and the Analytical values of their added mass coefficients are available, so that the results of added mass matrix are obtained and evaluated, using the boundary element method. Then the added mass matrix is computed in a given geometrical and flow specifications for a specific propeller and its results are studied versus experimental results, which it's current numerical data In comparison with other numerical methods has a good conformity with experimental results. The most important advantage of the method in determining the added mass matrix coefficients for the surface and underwater vessels and the marine propellers is extracting all the added mass coefficients with very good Accuracy, while in other numerical methods it is impossible to extract all the coefficients with the Desired Accuracy.

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