Adaptive Recompression of -Matrices for BEM

The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article, we use a hierarchical low-rank approximation, the so-called -matrix, that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low rank matrices. The low rank matrices are assembled by the ACA+ algorithm, an improved variant of the well-known ACA method. We present an algorithm that can determine a coarser block structure that minimises the storage requirements (enhanced compression) and speeds up the arithmetic (e.g., inversion) in the -matrix format. This coarse approximation is done adaptively and on-the-fly to a given accuracy such that the matrix is assembled with minimal storage requirements while keeping the desired approximation quality. The benefits of this new recompression technique are demonstrated by numerical examples.     

Adaptive multilevel rough entropy evolutionary thresholding

In this study, comprehensive research into rough set entropy-based thresholding image segmentation techniques has been performed producing new and robust algorithmic schemes. Segmentation is the low-level image transformation routine that partitions an input image into distinct disjoint and homogenous regions using thresholding algorithms most often applied in practical situations, especially when there is pressing need for algorithm implementation simplicity, high segmentation quality, and robustness. Combining entropy-based thresholding with rough set results in the rough entropy thresholding algorithm.The authors propose a new algorithm based on granular multilevel rough entropy evolutionary thresholding that operates on a multilevel domain. The MRET algorithm performance has been compared to the iterative RET algorithm and standard k-means clustering methods on the basis of β-index as a representative validation measure. Performance in experimental assessment suggests that granular multilevel rough entropy threshold based segmentations - MRET - present high quality, comparable with and often better than k-means clustering based segmentations. In this context, the rough entropy evolutionary thresholding MRET algorithm is suitable for specific segmentation tasks, when seeking solutions that incorporate spatial data features with particular characteristics.     

用无网格方法求解声波散射问题

在均匀介质中,对软表面障碍、时间调和声波散射问题归结为Helmholtz方程的Dirichlet外问题.应用无网格方法求解Helmholtz方程的Dirichlet外问题,并给出了一个数值例子,与Nystrom方法进行了对比,表明该方法是较精确的.     

Adaptive eigenspace for multi-parameter inverse scattering problems

A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation, each parameter is projected to a separate finite-dimensional subspace, which is iteratively adapted during the optimization. Each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori. The (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi-parameter problems, including the well-known Marmousi model from geosciences.     

Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences

We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which is constructed from a one-dimensional multiscale basis by the tensor product approach. Together with the use of hash tables as data structure, this allows in a simple way for adaptive refinement and is, due to the tensor product approach, well suited for higher dimensional problems. Also, the adaptive treatment of partial differential equations, the discretization (involving finite differences) and the solution (here by preconditioned BiCG) can be programmed easily. We describe the basic features of the method, discuss the discretization, the solution and the refinement procedures and report on the results of different numerical experiments.     

水声传感器网络节点自适应加权定位算法

对水声传感器网络节点定位进行研究,针对水声传感器网络节点间测距精度不高的问题,提出一种水声传感器网络节点自适应加权定位算法。考虑到水声传感器网络节点间的测距误差随着节点间距离的增大而增大,算法改进了锚节点选择机制,并且对不同锚节点在定位测度中的权重进行加权,改进定位测度,提高了测距信息的利用效率。仿真实验表明该算法提高了节点定位精度。     

Analysis of a conjugated infinite element method for acoustic scattering

This work is devoted to a study of a conjugated infinite element method for Helmholtz problems in exterior domains. A formulation of this method with Lagrange multipliers defined on (semi-)infinite space is presented and analyzed in a domain decomposition context. The implementation aspects of this method in a parallel industrial acoustic software (SYSNOISE) are described in details. Numerical results show the computational efficiency of this method on acoustic scattering problems.     

A GPGPU solution of the FMM near interactions for acoustic scattering problems

The Fast Multipole Method (FMM) is specially suitable for applications in which it is necessary to predict the acoustic scattering, e.g., aircraft noise control. This accelerated iterative method has two main parts, far interactions and near interactions. Near interactions are computationally intensive and they fit properly in the Single Instruction Multiple Threads paradigm. In this work, we present a heterogeneous parallel solution in which the near interactions are computed using Graphical Processing Units (GPUs). The performance of the proposed solution is proved using a workstation with one NVIDIA GTX480 GPU and a cluster that consists of 32 nodes HP BL465c with an Infiniband network.     

基于水声信道状态的自适应差错控制

水声信道具有时变、环境噪声高、传播时延大、信道带宽窄等特点,以致水声通信的可靠性不高(接收数据发生错误)。目前的解决办法主要有自动请求重传和前向纠错,但是这两种方式均不能在所有信道状态下保持较高的接收吞吐量。提出了一种自适应差错控择方法,其中包括一种利用信道误码率计算吞吐量的方法,并且采用自适应线性预测方法预测信道误码率,根据信道误码率选择合适的差错控制方式。仿真结果表明,采用该选择方法能够在所有的信道状态下保持较高的接收端吞吐量,提高水声通信的性能。     

Imaging of layered media in inverse scattering problems for an acoustic wave equation

Two-dimensional (2D) inverse scattering problems for the acoustic wave equation consisting of obtaining the density and acoustic impedance of the medium are considered. A necessary and sufficient condition for the unique solvability of these problems in the form of the law of energy conservation has been established. It is proved that this condition is that for each pulse oscillation source located on the boundary of a half-plane, the energy flow of the scattered waves is less than the energy flux of waves propagating from the boundary of this half-plane. This shows that for inverse dynamic scattering problems in acoustics and geophysics when the law of energy conservation holds it is possible to determine the elastic density parameters of the medium. The obtained results significantly increase the class of mathematical models currently used in solving multidimensional inverse scattering problems. Some specific aspects of interpreting inverse problems solutions are considered.     

Hierarchical LU Decomposition-based Preconditioners for BEM

The adaptive cross approximation method can be used to efficiently approximate stiffness matrices arising from boundary element applications by hierarchical matrices. In this article an approximative LU decomposition in the same format is presented which can be used for preconditioning the resulting coefficient matrices efficiently. If the LU decomposition is computed with high precision, it may even be used as a direct yet efficient solver.     

基于无线传感器网络的自适应声源定位算法

基于声源能量的无线传感器网络（ WSNs）最大似然定位算法抗噪声干扰能力强,定位精度高,同时适用于多个目标定位,但是计算量大,不适用于实时定位。针对现有算法的缺点,提出了一种基于自适应迭代的最大似然定位算法。该算法将代价函数作为目标函数,在给定的梯度误差范围内自适应地搜索目标位置。为了提高算法的收敛速度和定位精度,提出了基于Sigmoid函数的变步长的搜索算法。仿真实验结果表明：与最大似然定位算法相比,自适应迭代算法运算量小,定位精度高,能满足对目标定位精度和速度要求较高的场合,具有一定的实际应用意义。     

保形(Conformal)结构互连电容的BEM模拟

介绍了一种基于扫描线的复杂保形介质结构快速生成算法,该算法应用多边形的扩展运算和集合运算形成保形介质,同时处理保形介质听 凹槽,并已实现了边界元素法三维互连寄生电容提取软件B3D中,数值结果表明,该算法可靠,并有很高效率。     

Leader-follower strategies for multilevel systems

Sequential strategies for dynamic systems with multiple decision makers and multiple performance indices are surveyed and reviewed. These strategies are generalizations of Stackelberg or leader-follower strategies for two-person games. The review includes structures with one coordinator and several second-level decision makers, and linear hierarchical structures with only one decision maker at each level Several information structures are considered.     

Quadrature for parabolic Galerkin BEM with moving surfaces

The successful implementation of the Galerkin Boundary Element Method hinges on the accurate and effective quadrature of the influence coefficients. For parabolic boundary integral operators quadrature must be performed in space and time where integrals have singularities when source- and evaluation points coincide. For problems where the surface is fixed, the time integration can be performed analytically, but for moving geometries numerical quadrature in space and time must be used. For this case a set of transformations is derived that render the singular space–time integrals into smooth integrals that can be treated with standard tensor product Gauss quadrature rules. This methodology can be applied to the heat equation and to transient Stokes flow.     

3D BEM for the general piezoelectric solids

In this paper we present a new scheme of three-dimensional boundary element method for the general anisotropic piezoelectric solids. We use the Radon transform representation of the three-dimensional fundamental solutions of piezoelectricity and integrate them analytically over the triangular boundary element with the linear interpolation. This reduces the computation for the system matrices G and H from the standard singular surface integrations to the simple regular line integrations and enables a drastic reduction of the computation time. The integrand of the line integral consists of the product of a function dependent and another function independent on the location vectors representing the source and observation points. The latter function depends only on the material and element properties and thus calculated only once for each element and saved for a repeated use in the calculation of G and H matrices and in the post-processing. Exploitation of this favorable structure results in the further reduction of the computation time for very large systems. The implementation of the proposed method with numerical examples will be presented.     

A new BEM approach for reissner's plate bending

A new boundary element formulation for Reissner's plate bending is presented. This form of BEM has an advantage in that the bending stresses on the boundary can be calculated directly from the numerical solution, avoiding the use of tangential derivatives of displacement for finding plate bending stresses on the boundary. The effectiveness of the approach is also discussed through some test examples. In the present BEM formulation, the singular orders of the two kernels are the same as those in the standard BEM formulation of a Reissner's type plate—one of which is logarithmic singular and the other is 1/r singular.     

Distributed multilevel optimization for complex structures

Optimization problems concerning complex structures with many design variables may entail an unacceptable computational cost. This problem can be reduced considerably with a multilevel approach: A structure consisting of several components is optimized as a whole (global) as well as on the component level. In this paper, an optimization method is discussed with applications in the assessment of the impact of new design considerations in the development of a structure. A strategy based on fully stressed design is applied for optimization problems in linear statics. A global model is used to calculate the interactions (e.g., loads) for each of the components. These components are then optimized using the prescribed interactions, followed by a new global calculation to update the interactions. Mixed discrete and continuous design variables as well as different design configurations are possible. An application of this strategy is presented in the form of the full optimization of a vertical tail plane center box of a generic large passenger aircraft. In linear dynamics, the parametrization of the component interactions is problematic due to the frequency dependence. Hence, a modified method is presented in which the speed of component mode synthesis is used to avoid this parametrization. This method is applied to a simple test case that originates from noise control.     

Open source BEM library

This article presents the project of the new open source boundary element method library. It discusses main goals of the project and its characteristics consistent with the ‘good open source project’. It covers license conditions, chosen technology, design of the project as well as development process.