声学边界元方法中超奇异数值积分处理的新方法

利用正则化关系式处理了声学边界元方法中的超奇异数值积分。此正则化关系式经过数值离散化后,复合积分算子所对应的离散化系数矩阵被转化为构成该复合积分算子的两个积分算子所对应的离散化系数矩阵的乘积。从而形成了一种全新的处理超奇异数值积分的方法。为验证这一理论的正确性,文中给出了振荡球和脉动球声辐射数值算例。计算结果表明此方法效率高且数值解与解析解符合很好。     

大规模声学边界元法的GPU并行计算

提出一种大规模声学边界元法的高效率、高精度GPU并行计算方法.基于Burton-Miller边界积分方程,推导适于GPU的并行计算格式并实现了传统边界元法的GPU加速算法.为提高原型算法的效率,研究GPU数据缓存优化方法.由于GPU的双精度浮点运算能力较低,为了降低数值误差,研究基于单精度浮点运算实现的doublesingle精度算法.数值算例表明,改进的算法实现了最高89.8%的GPU使用效率,且数值精度与直接使用双精度数相当,而计算时间仅为其1/28,显存消耗也仅为其一半.该方法可在普通PC机(8GB内存,NVIDIA Ge Force 660 Ti显卡)上快速完成自由度超过300万的大规模声学边界元分析,计算速度和内存消耗均优于快速边界元法.     

基于Burton-Miller方程的轴对称结构声学边界元方法

提出了一种求取轴对称结构任意边界条件下声辐射特性的边界元方法。采用Burton和Miller改进型公式将高阶奇异项转化为弱奇异项之和,保证声辐射参数的唯一性,且计算简单精确。将结构表面声压与振速按照旋转轴角度进行Fourier级数展开,利用级数的正交性建立各项待定系数的求解公式;然后转化格林函数的法向偏导为切向偏导,方便直接计算各项积分,并将面积分公式表示为沿结构边界的线积分和沿旋转角度的积分;进一步采用二次等参单元离散结构边界线,建立声压与振速的关系矩阵,从而确定结构声辐射参数。以脉动球源和横向振动球源为例计算,与解析解和传统边界元法结果作对比,说明该方法的有效精确性。     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

改进型声学边界元级数多频算法

对于声学多频分析问题,研究者提出了一种声学边界元级数多频算法节省了重复计算频率无关项的时间,但这种原始算法受到多项式拟合的Runge现象限制,计算频段较窄。进一步改进此原始方法,提出了级数截断项数的选取原则,加入波数因子调整自变量区间避免Runge现象,消除了原始算法的不稳定性,拓展了级数多频算法的适用范围。声辐射计算实例证明了改进的级数多频算法的正确性,所需级数截断项数更少,降低了计算量,能够应用于更高频段的声学分析。     

某些位势问题的边界元方法

研究某些可归结为位势问题的边界元方法，先求边界元出发方程，经离散化后给出为数值模拟的计算机软件。计算结果符合物理规律并令人满意。     

二维声学多层快速多极子边界元及其应用

与模型自由度的平方成正比的存储量和计算量,使传统边界元无法应用到大型模型的计算。为此,发展了一种二维声学多层快速多极子边界元算法。通过二维Helmholtz核函数展开理论的简要介绍,推导了源点矩计算、源点矩转移、源点矩至本地展开转移、本地展开转移公式,并详细描述了二维声学快速多极子边界元算法的具体实现步骤。使用快速傅里叶插值进行源点矩和本地展开系数的多层传递。采用对角左预处理方法,改善边界方程的条件数,减少迭代求解次数。最后通过数值算例,验证了所发展的二维声学快速多极子算法的正确性和高效性。     

格子Boltzmann方法应用于气动声学研究

应用格子Boltzmann方法(LBM)对不同类型的气动声学问题进行数值研究.通过模拟一维平面声波和二维点源声波的传播,得到沿传播方向的声压脉动,其振荡幅值和衰减趋势与理论值相吻合.其次进行声波衍射和干涉现象的数值模拟.最后,模拟处于流场中运动声源辐射声场的多普勒效应.模拟结果说明LBM方法能较好地模拟低马赫数下的声学问题,包括声压脉动的传播,声波的波动特性以及流动与声波间的相互作用.     

Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed,by which the conventional and fast multipole BEMs(boundary element methods) for 3D acoustic problems based on constant elements are improved.To solve the problem of singular integrals,a Hadamard finite-part integral method is presented,which is a simplified combination of the methods proposed by Kirkup and Wolf.The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART(Projection and Angular Radial Transformation).The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab.In addition,the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution.The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations.A large-scale acoustic scattering problem,whose degree of freedoms is about 340,000,is implemented successfully.The results show that,the near singularity is primarily introduced by the hyper-singular kernel,and has great influences on the precision of the solution.The precision of fast multipole BEM is the same as conventional BEM,but the computational complexities are much lower.     

Numerical treatment of acoustic problems with boundary singularities by the singular boundary method

The singular boundary method (SBM) is a novel boundary-type meshless method based on the fundamental solution of the given governing equation. The SBM employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions. In this paper, we investigate the acoustic problems with boundary singularities using the SBM. This is achieved by combining the SBM with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution. The singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities. Then the regular solution is obtained by the SBM. Numerical examples show the excellent performance of the proposed technique.     

求解声辐射问题的微分求积法与微分求积单元法

基于无限域中的Helmholtz波动方程,将微分求积法与微分求积单元法应用于二维及三维声辐射问题的求解,对最外层节点施加不同阶数的人工边界条件,区域内使用均匀及非均匀的节点分布方式,分析了节点分布方式及人工边界条件对计算结果的影响,比较了两种数值方法的计算精度。研究结果表明:微分求积法与微分求积单元法,前者精度更高,而后者耗时更少,在频率较低时,具备较高的效费比。人工边界条件对计算结果的影响主要体现在低频段,而节点分布方式的影响主要体现在高频段。非均匀的节点分布方式在不同频段都具备更好的计算精度。     

Numerical difficulties with boundary element solutions of interior acoustic problems

Although boundary element methods have been applied to interior problems for many years, the numerical difficulties that can occur have not been thoroughly explored. Various authors have reported low-frequency breakdowns and artificial damping due to discretization errors. In this paper, it is shown through a simple example problem that the numerical difficulties depend on the solution formulation. When the boundary conditions are imposed directly, the solution suffers from artificial damping, which may potentially lead to erroneous predictions when boundary element methods are used to evaluate the performance of damping materials. This difficulty can be alleviated by first computing an impedance or admittance matrix, and then using its reactive component to derive the solution for the acoustic field. Numerical computations are used to demonstrate that this technique eliminates artificial damping, but does not correct errors in the reactive components of the impedance or admittance matrices, which then causes nonexistence and nonuniqueness difficulties at the interior resonance frequencies for hard-wall and pressure release boundary conditions, respectively. It is shown that the admittance formulation is better suited to boundary element computations for interior problems because the resonance frequencies for pressure release boundary conditions do not begin until the smallest dimension of the boundary surface is at least one half the acoustic wavelength. Aside from producing much more accurate predictions, the admittance matrix is also much easier to interpolate at low frequencies due to the absence of interior resonances. For the example problem considered, only the formulation using the reactive component of the admittance matrix produces accurate solutions as long as the surface element discretization satisfies the standard six-element-per-wavelength rule.     

Fast multipole accelerated boundary element method for the Helmholtz equation in acoustic scattering problems

We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficultie...     

Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

A conjugated infinite element method for half-space acoustic problems

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.     

On the instability of time-domain acoustic boundary element method due to the static mode in interior problems

In the analysis of interior acoustic problems, the time domain boundary element method (TBEM) suffers the monotonically increasing instability when using the direct Kirchhoff integral. This instability is related to the non-oscillatory static acoustic mode describing the constant spatial response in an enclosure. In this work, nonphysical natures of non-oscillatory static mode influencing the instability of TBEM calculation are investigated, and a method for stabilization is studied. In TBEM calculation, the static mode is represented by two non-oscillatory eigenmodes with different eigenvalues. The monotonically increasing instability is caused by the unstable poles of non-oscillatory eigenmodes as well as very small, very low frequency noise of an input signal. Interior problems with impedance boundary condition also exhibit the monotonically increasing instability stemming from its pseudo non-oscillatory static mode due to the lack of dissipation at very low frequencies. Calculation of transient sound fields within rigid and lined boxes provides numerical evidences. It is noted that the stabilization effort by modifying the coefficient matrix based on the spectral decomposition can be used only for correcting the unstable pole. The filtering method based on the eigen-analysis must be additionally used to avoid the remaining instability caused by very low frequency noise of input signal.