子结构FMBEM在消声器声场计算中的迭代收敛

子结构快速多极子边界元法融合了快速多极子算法、边界元法与子结构技术,使复杂结构声学问题的高效准确计算成为可能。然而对于不同的求解模型,其迭代收敛速度不稳定甚至不能收敛,直接影响了其在工程实际问题中的广泛应用。鉴于此,文章对子结构快速多极子边界元法,按照不同的矩阵构建及预处理方案分析其迭代收敛特性及影响因素。研究发现,除了采取恰当的矩阵预条件处理技术之外,未知量列向量的构建次序及边界节点编号顺序对迭代收敛速度有着重要影响;单步迭代时间随着计算频率的增大而呈指数增长。此外,以内插管型消声器传递损失的计算为例,通过与实验值的比较证实了该方法的准确性与有效性。     

快速多极与常规边界元法机群并行计算的比较

以三维弹性力学问题为例,对快速多极与常规边界元法机群并行计算进行了比较。其中常规边界元法求解方程采用高斯消去法,通过调用标准并行求解函数库ScaLAPACK实现;快速多极边界元法并行计算程序采用ANSIC++语言、调用MPI并行通信库自行编写。两种程序均运行于同一机群并行环境。数值算例表明,在同样的机群条件下,采用快速多极边界元法可使解题规模有数量级的提高,计算速度明显高于常规边界元法,并行效率也优于常规边界元法。     

激光干涉仪反射镜三维温度场的快速多极边界元分析

温差造成光刻机激光干涉仪反射镜热变形,从而影响光刻机的精度。该文将基于二次单元的快速边界元法用于激光干涉仪反射镜的大规模温度场模拟。不连续单元的引入可以有效处理角点问题;新型快速多极算法用于边界元法的加速求解。建立统一的二次单元多极展开格式以处理混合边界。数值算例分析了快速多极边界元法的计算精度和效率,并和常规算法比较;使用该算法对激光干涉仪反射镜进行了大规模温度场计算,并和有限元法比较。结果表明:基于二次单元的快速多极边界元法可以高精度求解大规模三维传热问题。     

快速多极边界元法在大规模传热分析中的应用

该文将快速多极边界元法用于三维稳态传热问题的大规模数值计算。多极展开的引入使得该算法能够在单台个人电脑上完成30万自由度以上的传热边界元分析。统一展开的基本解能够处理混合边界。广义极小残差法作为快速多极边界元法的迭代求解器,数值算例分析了快速多极边界元法的计算效率。结果表明:快速多极边界元法的求解效率与常规算法相比有数量级的提高;在模拟复杂结构大规模传热问题上将具有良好的应用前景。     

快速多极子边界元法在吸声材料声场计算中的应用

对快速多极子边界元法中多极子展开式的数值计算进行了研究,建立四点单级传递关系与多极传递关系模型。通过与格林函数及其法向导数理论值的比较,考察两种传递情况下,多极子展开式在吸声材料介质及空气介质中的计算精度。结果表明,复波数展开式的求解精度与截断项数的大小相关,而且当复波数虚部值与展开点间距离乘积过大时,展开式值开始与真值相背离。最后提出了解决此问题的两种方法。此外,以膨胀腔阻性消声器传递损失计算为例,验证了本文方法的有效性与可行性。     

二维新型快速多极虚边界元配点法

以二维弹性问题为研究背景, 提出了一种二维新型快速多极虚边界元配点法的求解思想, 即采用新型的快速多极展开和运用广义极小残值法来求解传统的虚边界元配点法方程。相对常规快速多极展开技术, 该文针对二维弹性问题在原有的快速多极虚边界元法展开格式的基础上, 通过引入对角化的概念, 以更新展开传递格式, 欲达到进一步提高计算效率的目的。数值算例说明了该方法的可行性, 计算效率和计算精度。此外, 该文方法的思想具有一般性, 应用上具有扩展性。     

基于有限元与宽频快速多极边界元的二维流固耦合声场分析

采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。     

基于FEM/BEM法的模拟舱室结构声辐射仿真与试验

针对机舱结构辐射噪声问题,基于有限元/边界元法,对模拟舱室结构进行辐射声场仿真与试验。首先建立模拟舱室结构的有限元模型,对模拟舱室结构进行模态试验,将仿真计算与模态试验进行对比,验证了有限元模型的正确性。然后进行模拟舱室结构的声辐射试验,得到模拟舱室结构内部的声压频响特性。最后在ANSYS中对模拟舱室结构进行瞬态响应计算,将结构受节点力激励的响应导入Virtual Lab中,采用间接边界元法计算空腔结构内部的辐射声场。仿真与试验有较好的一致性,表明该方法是正确、可行的。     

海洋平台上噪声分析方法

以海洋平台上动力设备产生的大量振动噪声为研究对象,阐述海洋平台和FPSO等结构物声振耦合分析的数值方法以及噪声分析的相关软件。海洋平台上的噪声传播有空气声传播和结构声传播两种传播路径,计算分析时均需要考虑。快速多极边界元法是未来噪声分析的有效方法。     

一种高效的发动机辐射噪声计算方法研究

为了解决发动机辐射噪声计算的精度和效率问题,基于表面速度振动原理,利用Matlab程序,开发了一种高效的发动机辐射噪声声功率模拟计算软件。分别用边界元法、快速多级边界元法和Matlab程序软件对比分析了普通平板、发动机缸盖罩和发动机动力总成辐射声功率的计算精度和效率,结果显示,在保证高的计算精度情况下,用Matlab程序软件计算发动机缸盖罩辐射声功率的效率是边界元法的25倍,是快速多级边界元法的123倍;用Matlab程序软件计算发动机动力总成辐射声功率的效率是边界元法的141倍,是快速多级边界元法的108倍。     

A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems

A low-frequency fast multipole boundary element method (FMBEM) for 3D acoustic problems is proposed in this paper. The FMBEM adopts the explicit integration of the hypersingular integral in the dual boundary integral equation (BIE) formulation which was developed recently by Matsumoto, Zheng et al. for boundary discretization with constant element. This explicit integration formulation is analytical in nature and cancels out the divergent terms in the limit process. But two types of regular line integrals remain which are usually evaluated numerically using Gaussian quadrature. For these two types of regular line integrals, an accurate and efficient analytical method to evaluate them is developed in the present paper that does not use the Gaussian quadrature. In addition, the numerical instability of the low-frequency FMBEM using the rotation, coaxial translation and rotation back (RCR) decomposing algorithm for higher frequency acoustic problems is reported in this paper. Numerical examples are presented to validate the FMBEM based on the analytical integration of the hypersingular integral. The diagonal form moment which has analytical expression is applied in the upward pass. The improved low-frequency FMBEM delivers an algorithm with efficiency between the low-frequency FMBEM based on the RCR and the diagonal form FMBEM, and can be used for acoustic problems analysis of higher frequency.     

A fast multipole boundary element method for 3D multi-domain acoustic scattering problems based on the Burton-Miller formulation

A fast multipole boundary element method (FMBEM) for 3D multi-domain acoustic scattering problems based on the Burton-Miller formulation is presented in this paper. A multi-tree structure is designed for the multi-domain FMBEM. It results in mismatch of leaves and well separate cells definition in different domains and complicates the implementation of the algorithm, especially for preconditioning. A preconditioner based on boundary blocks is devised for the multi-domain FMBEM and its efficiency in reducing the number of iterations in solving large-scale multi-domain scattering problems is demonstrated. In addition to the analytical moment, another method, based on the anti-symmetry of the moment kernel, is developed to reduce the moment computation further by a factor of two. Frequency sweep analysis of a penetrable sphere shows that the multi-domain FMBEM based on the Burton-Miller formulation can overcome the non-unique solution problem at the fictitious eigenfrequencies. Several other numerical examples are presented to demonstrate the accuracy and efficiency of the developed multi-domain FMBEM for acoustic problems. In spite of the high cost of memory and CPU time for the multi-tree structure in the multi-domain FMBEM, a large BEM model studied with a PC has 0.3 million elements corresponding to 0.6 million unknowns, which clearly shows the potential of the developed FMBEM in solving large-scale multi-domain acoustics problems.     

An Adaptive Fast Multipole Boundary Element Method for Three-dimensional Potential Problems

An adaptive fast multipole boundary element method (FMBEM) for general three-dimensional (3-D) potential problems is presented in this paper. This adaptive FMBEM uses an adaptive tree structure that can balance the multipole to local translations (M2L) and the direct evaluations of the near-field integrals, and thus can reduce the number of the more costly direct evaluations. Furthermore, the coefficients used in the preconditioner for the iterative solver (GMRES) are stored and used repeatedly in the direct evaluations of the near-field contributions. In this way, the computational efficiency of the adaptive FMBEM is improved significantly. The adaptive FMBEM can be applied to both the original FMBEM formulation and the new FMBEM with diagonal translations. Several numerical examples are presented to demonstrate the efficiency and accuracy of the adaptive FMBEM for studying large-scale 3-D potential problems. The adaptive FMBEM is found to be about 50% faster than the non-adaptive version of the new FMBEM in solving the model (with 558,000 elements) for porous materials studied in this paper. The computational efficiencies and accuracies of the FMBEM as compared with the finite element method (FEM) are also studied using a heat-sink model. It is found that the adaptive FMBEM is especially advantageous in modeling problems with complicated domains for which free meshes with much more finite elements would be needed with the FEM.     

A fast multipole boundary element method based on the improved Burton–Miller formulation for three-dimensional acoustic problems

A fast multipole boundary element method (FMBEM) based on the improved Burton–Miller formulation is presented in this paper for solving large-scale three-dimensional (3D) acoustic problems. Some improvements can be made for the developed FMBEM. In order to overcome the non-unique problems of the conventional BEM, the FMBEM employs the improved Burton–Miller formulation developed by the authors recently to solve the exterior acoustic problems for all wave numbers. The improved Burton–Miller formulation contains only weakly singular integrals, and avoids the numerical difficulties associated to the evaluation of the hypersingular integral, it leads to the numerical implementations more efficient and straightforward. In this study, the fast multipole method (FMM) and the preconditioned generalized minimum residual method (GMRES) iterative solver are applied to solve system matrix equation. The block diagonal preconditioner needs no extra memory and no extra CPU time in each matrix–vector product. Thus, the overall computational efficiency of the developed FMBEM is further improved. Numerical examples clearly demonstrate the accuracy, efficiency and applicability of the FMBEM based on improved Burton–Miller formulation for large-scale acoustic problems.     

An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation

The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multipole boundary element method (FMBEM) based on the Burton–Miller formulation for 3-D acoustics is presented in this paper. In this adaptive FMBEM, the Burton–Miller formulation using a linear combination of the CBIE and hypersingular BIE (HBIE) is applied to overcome the non-uniqueness difficulties. The iterative solver generalized minimal residual (GMRES) and fast multipole method (FMM) are adopted to improve the overall computational efficiency. This adaptive FMBEM for acoustics is an extension of the adaptive FMBEM for 3-D potential problems developed by the authors recently. Several examples on large-scale acoustic radiation and scattering problems are presented in this paper which show that the developed adaptive FMBEM can be several times faster than the non-adaptive FMBEM while maintaining the accuracies of the BEM.     

Fast multipole boundary element approaches for acoustic attenuation prediction of reactive silencers

The fast multipole boundary element method (FMBEM) is applied to predict the acoustic attenuation performance of reactive silencers. In order to overcome the difficulty of singular boundaries for the acoustic computation of reactive silencers with internal thin wall structure or/and perforated components, two approaches, the substructure FMBEM (Sub-FMBEM) and mixed-body FMBEM (MB-FMBEM) are proposed, and the theoretical foundations and numerical processes of the both approaches are introduced. The studies demonstrated that the ordering of column vectors and numbering of nodes in the Sub-FMBEM have great influence on the convergence of iteration, and the MB-FMBEM may reduce the number of elements and the computational complexity since it only needs to discretize one side boundary of the thin wall and perforated components and it is not necessary to create the interfaces. The Sub-FMBEM, MB-FMBEM and Sub-BEM are then employed to calculate the transmission loss of reactive silencers with thin wall components and perforated tubes, the computational accuracy and efficiency of the approaches are validated. The data of precomputing time and total iterative computational time demonstrated that, the computational efficiency of Sub-FMBEM will descend as the frequency arising, and the Sub-FMBEM may reveal higher computational efficiency than Sub-BEM only when the number of nodes is big enough.     

hp Fast multipole boundary element method for 3D acoustics

A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three‐dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h‐p mesh refinement strategy enables accurate computation of large‐scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. Copyright © 2016 John Wiley & Sons, Ltd.     

An adaptive dual-information FMBEM for 3D elasticity and its GPU implementation

Combined the boundary element method (BEM) with the fast multipole method (FMM), the fast multipole BEM (FMBEM) is proposed to solve large scale problems. A key issue the FMBEM has to address is the element integrals, which usually consumes much time when the FMM for N-body problems is directly used. In order to accelerate element integrals, we present an adaptive FMBEM with a particular dual-information tree structure which contains both node and element information, and use it for 3D elasticity in this paper. In our adaptive FMBEM, the Multipole Expansions (ME), Moment-to-Local (M2L) translation, Local Expansions (LE), and the Near Field Direct Computation (NFDC) are level independent so that they are suitable for parallel computing. The examples show that the time of ME and NFDC in our FMBEM is almost 1/3 and 1/2 compared with that in a node-based FMBEM which deals with FMBEM in a particle interaction mode. We develop two GPU parallel strategies to accelerate the processes of ME, M2L and NFDC and implement them on a NVIDIA GTX 285 GPU, and the speedups to an Intel Core2 Q9550 CPU using 4 cores can reach 10.7 for ME, 16.2 for M2L, and 3.6 for NFDC.