运动介质中奇异边界元积分式的精确求解

采用边界元方法求解与运动介质相关声学问题时,难点之一是如何精确计算场点与源点重合所导致的奇异积分式。论文提出一种将具有奇性的单元面积分式拆分为奇性和非奇性积分部分分别进行计算的新方法。对奇性积分部分,经过严格的数学推导给出解析解;而对非奇性积分部分则通过高斯积分法处理。新方法可有效地提高边界元计算精度和效率,对运动介质中的有关声学问题的边界元数值计算具有重要意义。     

Helmholtz声学边界积分方程中奇异积分的计算

提出了一种非等参单元的四边形坐标变换,它将积分的曲面单元映射为另一四边形单元,通过两次坐标变换引入的雅可比行列式可以消除Helmholtz声学边界积分方程中的弱奇异型O(1／r))积分．而且利用δr／δn以及坐标变换可以同时消除坐标变换无法消除的Cauchy型(O(1／r^2))奇异积分,并给出了消除奇异性的详细证明．该方法给Helmholtz声学边界积分方程中的弱奇异积分与Cauchy奇异积分的计算以及编程提供了极大便利。     

齿轮泵声辐射性能仿真分析与结构优化

在软件Hypermesh中建立齿轮泵结构有限元模型,提取其结构模态;在软件LMS. Virtual. Lab中,结合齿轮泵的模态,得出泵体模态的频率响应和节点加速度;在声学边界元模块中,利用直接边界元法计算标准场点处的声学响应;分析得出泵的声辐射性能与其模态振型相关,提出结构改进方案,以改善模态振型,从而降低泵的辐射噪声。     

声学边界元拟奇异积分计算的自适应方法

提出一种自适应方法计算声学边界元中的拟奇异积分,通过单元分级细分将总积分转移到子单元上以消除拟奇异性。在此方法基础上深入研究拟奇异性,进一步提出接近度的概念,其中临界接近度可作为拟奇异积分计算的理论依据,并可用于预估拟奇异性是否存在。此方法的积分精度可调控,且不受场点位置限制,相比于已有方法更加灵活高效。数值分析表明拟奇异性强弱由场点与单元的相对位置决定,单元上远离场点的区域拟奇异性很弱,无需处理。研究结果为处理边界元法中的拟奇异性问题提供了新的选择和参考。     

四边形常数单元离散下的声学非奇异BIE

奇异积分是基于Burton-Miller方程的声学边界元法实现过程的难点之一。关于三角形单元离散的积分单元的已经比较成熟,研究四边形常数单元离散下的声学边界积分方程(BIE),通过构造围绕配点的极小半球面进行积分,求得积分中的发散项,推导四边形常数单元离散下边界积分方程及其法向求导的非奇异表达式,从而得到非奇异Burton-Miller方程。运用Gauss Legendre积分公式计算BIE的S(x)的数值解,对比解析解的计算结果,得出了数值解、解析解以及二者的绝对误差、相对误差随ka的变化规律。实际应用时,当给定精度和ka的值后,可以通过改变所需要的截断项数,使得误差满足给定的精度要求。     

声学-结构设计灵敏度分析

声学 -结构设计灵敏度分析揭示了结构振动引起的辐射声压与结构设计变量之间的关系。分别用有限元法和边界元法计算结构设计灵敏度和声学灵敏度。将两个灵敏度结合得到最终的声学 -结构设计灵敏度。在边界元计算中 ,采用退化元处理奇异积分问题 ,对特征频率不唯一问题采用CHIEF方法处理。以脉动球和箱体为例 ,验证了算法的可行性和精确性。     

边界元法在环境声学中的应用

边界元法是边界积分方程的数值解法 ,是随着计算机技术的发展而出现的。建立声学边界积分方程分两种方法 :直接法与间接法。本文介绍了边界元法在环境声学中的应用 ,如声屏障和不同情况下道路周围的声场分布、复杂气象条件对声传播的影响的问题等。由于边界元法是半解析半数值解法。在解边界积分方程时会遇到解的存在与唯一性问题。     

二维边界元法中几乎奇异积分的解析法

边界元分析中的几乎奇异积分难题一直阻碍其在工程中应用。作者提出的半解析法有效计算了几乎奇异积分,在此基础上做进一步推演,得到线性单元和二次亚参元上几乎强奇异和超奇异积分的解析列式,摈弃了数值求积。该算式对高次单元也近似适用。这个算法使得边界元法能够分析弹性力学薄壁结构。     

简支梁在无限大不可压缩流体和声学流体中的固有振动问题

本文用边界积分方程描述无限大声学流体,从而得到了控制圆截面简支梁在该流体中固有振动的积分-微分方程。在此方程基础上,分别用摄动法和有限元与摄动展开相结合的方法,计算了简支梁在无限大声学流体中的固有频率。当声速趋于无穷大时,得到了无限大不可压缩流体中简支梁的固有频率。本文的方法可推广到较为复杂的结构声辐射系统的固有频率的计算上。     

有限元/边界元方法在卡车驾驶室声学分析中的应用

利用有限元分析软件ANSYS和边界元分析软件SYSNOISE对卡车驾驶室的振动与内部声辐射做了数值计算分析研究.应用ANSYS软件建立了驾驶室有限元分析模型,说明了振动频响分析方法,动力学计算结果与声学边界元模型耦合的具体步骤.介绍了如何应用SYSNOISE软件建立驾驶室三维边界元声学分析模型,并采用直接边界元法,对驾驶室振动声学特性进行了计算分析.     

轴对称声振耦合的边界子波谱与有限元耦合方法及应用

在轴对称结构有限元和轴对称Helmholtz积分方程的基础上,建立了轴对称弹性结构构声振耦合的边界 子波谱有限元耦合方法,该方法能处理任意边界条件。采用提出的耦合方法研究了含有壳、肋、板复杂结构的水下航行 器的声辐射,给出了轴对称圆环肋的刚度矩阵和质量矩阵。进行了声振耦合的模态分析,研究了航行器的轴向激励、侧 向激励的声辐射;计算了0～2kHz的频率响应。结果对水下航行器的研究设计有一定的参考价值。     

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

In this paper, a new effective boundary node method is presented for the solution of acoustic problems, directly in time domain, using exponential basis functions. Unlike many other methods using boundary information, the final coefficient matrix is sparse. The formulation is well suited for domains whose extent is relatively larger than the distance traveled by the acoustic wave in an increment of time. The exponential basis functions used satisfy the time‐space governing equation. This helps to choose a relatively large time increment and a moderate number of boundary points, which leads to reduction of computation time. The computation is performed incrementally using a weighted residual in time. Through a series of numerical examples, it is shown that the method, when combined with a domain decomposition strategy, is effectively capable of solving various 1‐ to 3‐dimensional acoustic problems.     

An h-hierarchical Galerkin BEM using Haar wavelets

Application of Haar wavelet to h-hierarchical adaptive method is attempted to improve the performance. The wavelet boundary element method (BEM) is developed by means of the Galerkin method. In order to save memory requirement and computation time, sparse matrices are obtained by truncation of matrix coefficients. Error indicator and estimator are constructed based on the difference between the true solution and its projection onto the mesh. These values are effectively evaluated using the boundary element solution. The adaptive method is developed for 2D Laplace problems. Through numerical examples, performance of the present method is investigated concerning the sparseness of matrices and the computation time devoted to calculation of matrix coefficients and to equation solving process.     

Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method

This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and hypersingular boundary integrals contained in the equations are evaluated as the Cauchy principal values and Hadamard finite parts for constant element discretization without using any regularization technique in this study. The present boundary integral equations are more efficient to use than the usual ones based on any other singularity subtraction technique and can be applied to the fast multipole boundary element method more readily and efficiently. The effectiveness and accuracy of the present equations are demonstrated through some numerical examples.     

非协调单元在声学边界元法中的应用

利用非协调元离散Helmholtz边界积分方程,有效地解决协调元计算中的角点问题。为消除积分奇异性,提出了非协调元法中的极坐标变换方法。采用CHIEF法加Lagrange乘子法进行处理特征频率处解的不唯一性。解线性代数方程组获得结点处声压,网格点处的声压通过结点平均或单元平均的方法计算。通过计算脉动球和立方体的表面辐射声压,并将协调元和非协调元的计算结果做了比较,证明本文方法的有效性和对非光滑表面的适应性。     

On the use of piecewise linear wavelets for fast construction of sparsified moment matrices in solving the thin-wire EFIE

Multiresolution wavelet expansion technique has been successfully used in the method of moments (MoM), and sparse matrix equations have been attained. Solving boundary integral equations arising in electromagnetic (EM) problems by the wavelet-based moment method (WMM) involves a time-consuming double numerical integration for each entry of the resultant matrix which in turn can outweigh the advantages of achieving a sparse matrix. The paper presents an alternative computational model to speed up the WMM by excluding double numerical integrations in the evaluation of matrix elements. In this regard, pieces of linear wavelet bases are replaced by proper sinusoidal functions for which closed-form analytical expressions are available. In addition, by introducing approximate closed-form expressions for radiating EM fields of wavelet current elements, the thresholding procedure is modified so that one can compute only the matrix elements of interest. To demonstrate the effectiveness of the proposed method, the thin-wire electric field integral equation (EFIE) is numerically solved by non-orthogonal linear spline wavelet bases.     

APPLICATION OF WAVELETS ON THE INTERVAL TO NUMERICAL ANALYSIS OF INTEGRAL EQUATIONS IN ELECTROMAGNETIC SCATTERING PROBLEMS

The wavelet expansions on the interval are employed for solving the problems of the electromagnetic (EM) scattering from two-dimensional (2-D) conducting objects. The arbitrary configurations of scatterers are modeled using the boundary element method (BEM). By using the wavelets on the interval as basis and test functions, a sparse matrix equation is generated from the integral equation under study. The resulted sparse matrix equation allows the use of sparse matrix solvers or multi-level iterations for rapid solution. The utilization of wavelets on the interval circumvents the difficulties in the application of the wavelets on the real line to finite interval problems, and has no periodicity constraint to the unknown function that is usually imposed by periodic wavelets. Numerical examples are provided and compared with the previously published data or other methods. © 1997 by John Wiley & Sons, Ltd.     

Boundary spectral methods for non-lifting potential flows

The boundary spectral method for solving three-dimensional non-lifting potential problems is developed. This method combines spectral approximations and the direct numerical integration such as Gaussian quadrature or trapezoidal rules successfully. The singularities of the integral equation are completely removed by subtracting known solutions from the Laplace equation. After discretization, every element of the resultant matrix only contains integrals with non-singular kernels. Therefore, all the integrals can be implemented easily and efficiently. By spectral approximations, the unknown variable is expressed as a truncated series of basis functions, which are orthogonal usually. Instead of solving the variables at collocation points in the conventional methods, the coefficients of basis functions are determined in the spectral approach. It is shown that the new method reduces a lot of number of unknowns, storage of matrix elements, and computer time for solving the algebraic equations. © 1998 John Wiley & Sons, Ltd.     

Analytical integration of the moments in the diagonal form fast multipole boundary element method for 3-D acoustic wave problems

A diagonal form fast multipole boundary element method (BEM) is presented in this paper for solving 3-D acoustic wave problems based on the Burton-Miller boundary integral equation (BIE) formulation. Analytical expressions of the moments in the diagonal fast multipole BEM are derived for constant elements, which are shown to be more accurate, stable and efficient than those using direct numerical integration. Numerical examples show that using the analytical moments can reduce the CPU time by a lot as compared with that using the direct numerical integration. The percentage of CPU time reduction largely depends on the proportion of the time used for moments calculation to the overall solution time. Several examples are studied to investigate the effectiveness and efficiency of the developed diagonal fast multipole BEM as compared with earlier p³ fast multipole method BEM, including a scattering problem of a dolphin modeled with 404,422 boundary elements and a radiation problem of a train wheel track modeled with 257,972 elements. These realistic, large-scale BEM models clearly demonstrate the effectiveness, efficiency and potential of the developed diagonal form fast multipole BEM for solving large-scale acoustic wave problems.     

A gradient free integral equation for diffusion–convection equation with variable coefficient and velocity

In this paper a boundary-domain integral diffusion–convection equation has been developed for problems of spatially variable velocity field and spatially variable coefficient. The developed equation does not require a calculation of the gradient of the unknown field function, which gives it an advantage over the other known approaches, where the gradient of the unknown field function is needed and needs to be calculated by means of numerical differentiation. The proposed equation has been discretized by two approaches—a standard boundary element method, which features fully populated system matrix and matrices of integrals and a domain decomposition approach, which yields sparse matrices. Both approaches have been tested on several numerical examples, proving the validity of the proposed integral equation and showing good grid convergence properties. Comparison of both approaches shows similar solution accuracy. Due to nature of sparse matrices, CPU time and storage requirements of the domain decomposition are smaller than those of the standard BEM approach.