A new fast multipole boundary element method for two dimensional acoustic problems

A new fast multipole boundary element method (BEM) is presented in this paper for solving large-scale two dimensional (2D) acoustic problems based on the improved Burton–Miller formulation. This algorithm has several important improvements. The fast multipole BEM employs the improved Burton–Miller formulation, and successfully overcomes the non-uniqueness difficulty associated with the conventional BEM for exterior acoustic problems. 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. Furthermore, the fast multipole method (FMM) and the approximate inverse preconditioned generalized minimum residual method (GMRES) iterative solver are adopted to greatly improve the overall computational efficiency. The numerical examples with Neumann boundary conditions are presented that clearly demonstrate the accuracy and efficiency of the developed fast multipole BEM for solving large-scale 2D acoustic problems in a wide range of frequencies.     

Fast multipole method based solution of electrostatic and magnetostatic field problems

Abstact Applications of boundary element methods (BEM) to the solution of static field problems in electrical engineering are considered in this paper. The choice of a suitable BEM formulation for electrostatics, steady current flow fields or magnetostatics is discussed from user's point of view. The dense BEM matrix is compressed with an enhanced fast multipole method (FMM) which combines well-known BEM techniques with the FMM approach. An adaptive grouping scheme for problem oriented meshes is presented along with a discussion on the influence of the mesh to the efficiency of the FMM. The computational costs of the FMM algorithm are analyzed for typical problems in practice. Finally, some electrostatic and magnetostatic numerical examples demonstrate the simple usability and the efficiency of the FMM. Communicated by: U. Langer     

层次式直接边界元计算VLSI三维互连电容

文中将Ａｐｐｅｌ处理多体问题的层次式算法思想实现于直接边界元法,用以计算ＶＬＳＩ三维互连寄生电容。直接边界积分方程同时含有边界上的电势与法向电场强度,能比间接边界元法更方便地处理多介质及有限介质结构,直接边界元法的层次式计算涉及对三种边界（强加边界、自然边界与介质交界面）及两种积分核（１／ｒ与１／ｒ＾３）的处理,显著区别于基于间接边界元法、仅处理强加边界与一种分核的层次式算法。文中以边界元的层次划     

A linear Uzawa-type FEM–BEM solver for nonlinear transmission problems

We propose a fully discrete Uzawa-type iteration for the Johnson–Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular integral equation associated with the Laplace-operator and one FEM for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to build the right-hand side of the Yukawa equation. The algorithm includes the inexact solution of the BEM/FEM part by a preconditioned CG method. We prove that the proposed method leads to linear convergence with respect to the number of Uzawa iterations. Moreover, while the current analysis of a direct FEM–BEM discretization of the Johnson–Nédélec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.     

并行计算水下大尺度弹性壳体的低频声散射

有限元与边界元耦合模型是研究水下弹性壳体目标低频声散射常用的数值方法。应用该模型计算大尺度弹性目标的声散射时需要大量的计算时间与存储空间,采用并行数值的方式可以解决这一问题。首先并行计算生成有限元矩阵和边界元矩阵,然后应用并行化的广义极小残差(GMRES)迭代算法求解大型非对称线性方程组。详细叙述了并行GMRES(m)迭代算法的执行过程,并以球壳的声散射计算为例分析了迭代步数对算法收敛情况的影响。最后计算了Benchmark目标模型的低频散射声场,分析了其收发分置散射目标强度以及表面声场的分布。     

The mapping method as a toolbox to analyze,design, and optimize micromixers

The mapping method is employed as an efficient toolbox to analyze, design, and optimize micromixers. A new and simplified formulation of this technique is introduced here and applied to three micromixers: the staggered herringbone micromixer (SHM), the barrier-embedded micromixer (BEM), and the three-dimensional serpentine channel (3D-SC). The mapping method computes a distribution matrix that maps the color concentration distribution from inlet to outlet of a micromixer to characterize mixing in a quantitative way. Once the necessary distribution matrices are obtained, computations are fast and numerous layouts of the mixer are easily evaluated, resulting in an optimal design. This approach is demonstrated using the SHM and the BEM as typical examples. Mixing analysis in the 3D-SC illustrates that also complex flows, for example in the presence of back-flows, can be efficiently dealt with by using the new formulation of the mapping method.     

二维熵阈值法的修改及其快速迭代算法

提出二维熵阈值法的一种修改方法和其快速迭代算法。针对传统二维熵阈值法及其递推算法的高计算复杂性的不足,首先对二维直方图所对应的二元概率分布进行修改并得到一种新的二维熵阈值法。其次假设二维直方图所对应的二元概率分布是连续可微的条件下导出的修改后的二维熵阈值法的快速迭代算法。实验结果表明,文中提出的修改二维熵阈值法及其快速迭代算法是可行的,且快速迭代算法的时间消耗相对其递归算法有很大程度地降低。     

Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems

This paper describes the parallelization of a strategy to speed up the convergence of iterative methods applied to boundary element method (BEM) systems arising from problems with non-smooth boundaries and mixed boundary conditions. The aim of the work is the application of fast wavelet transforms as a black box transformation in existing boundary element codes. A new strategy was proposed, applying wavelet transforms on the interval, so it could be used in case of non-smooth coefficient matrices. Here, we describe the parallel iterative scheme and we present some of the results we have obtained.     

GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method

An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.     

An optimised FEM–BEM time-domain iterative coupling algorithm for dynamic analyses

In the present work, an optimised FEM–BEM iterative coupling algorithm is presented, regarding time-domain dynamic applications. The methodology allows non-linear behaviour to be easily considered within sub-domains modelled by the FEM, as well as independent time discretizations to be considered within each sub-domain. By minimizing a square error functional, an optimised expression is obtained to evaluate the iterative coupling relaxation parameter, increasing the efficiency of the FEM–BEM coupled analysis directly accomplished in the time-domain. At the end of the paper, numerical applications are presented, illustrating the potentialities of the proposed methodology.     

A design technique for fast sampled-data nonlinear model predictive control with convergence and stability results

ABSTRACT

In this study, a sampled-data nonlinear model predictive control scheme is developed. The control algorithm uses a prediction horizon with variable length, a terminal constraint set, and a feedback controller defined on this set. Following a suboptimal solution strategy, a defined number of steps of an iterative optimisation routine improve the current input trajectory at each sampling point. The value of the objective function monotonically decreases and the state converges to a target set. A discrete-time formulation of the algorithm and a discrete-time design model ensure high computational efficiency and avoid an ad hoc quasi-continuous implementation. This design technique for a fast sampled-data nonlinear model predictive control algorithm is the main contribution of the paper. Based on a benchmark control problem, the performance of the developed control algorithm is assessed against state-of-the-art nonlinear model predictive control methods available in the literature. This assessment demonstrates that the developed control algorithm stabilises the system with very low computational effort. Hence, the algorithm is suitable for real-time control of fast dynamical systems.     

基于BFGS计算力场的GVF Snake模型及其应用实现

梯度向量流模型(GVF Snake)在图像处理领域取得较好的效果.但它简单的迭代运算方法,其收敛速度慢,限制了其应用.针对梯度向量场的计算,提出一种基于BFGS算法求解力场的方法,给出详细的求解过程并并且通过计算机仿真进行数值求解,最后将改进后的GVF Snake模型用于图像处理.结果表明, BFGS-GVF建立的梯度向量场性能较好.与图像处理中的牛顿几何轮廓算法、CV活动轮廓算法及IALM-GVF Snake算法进行对比, BFGS-GVF Snake算法能得到清晰、光滑的图像轮廓.     

A continuous-time integrated model for discrete control of production flows in a multi-level bills of material environment

An integrated dynamic model for discrete production scheduling and continuous capacity expansion is presented in this paper. The modeled manufacturing system, based on multi-level bills of materials, is characterized by flexible machines with negligible setups and production rates fixed for the current capacity. Make-to-stock formulation of the problem is studied and optimal behavior of the system is determined with the help of the maximum principle. A fast time-decomposition algorithm is suggested to locate the optimal solution.     

A genetic algorithm for MRF-based segmentation of multi-spectral textured images

A segmentation approach based on a Markov random field (MRF) model is an iterative algorithm; it needs many iteration steps to approximate a near optimal solution or gets a non-suitable solution with a few iteration steps. In this paper, we use a genetic algorithm (GA) to improve an unsupervised MRF-based segmentation approach for multi-spectral textured images. The proposed hybrid approach has the advantage that combines the fast convergence of the MRF-based iterative algorithm and the powerful global exploration of the GA. In experiments, synthesized color textured images and multi-spectral remote-sensing images were processed by the proposed approach to evaluate the segmentation performance. The experimental results reveal that the proposed approach really improves the MRF-based segmentation for the multi-spectral textured images.     

Fast evaluation of vector splines in three dimensions

Vector spline techniques have been developed as general-purpose methods for vector field reconstruction. However, such vector splines involve high computational complexity, which precludes applications of this technique to many problems using large data sets. In this paper, we develop a fast multipole method for the rapid evaluation of the vector spline in three dimensions. The algorithm depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation. In comparison with the CPU time of direct calculation, which increases at a quadratic rate with the number of points, the presented fast algorithm achieves a higher speed in evaluation at a linear rate. The theoretical error bounds are derived to ensure that the fast method works well with a specific accuracy. Numerical simulations are performed in order to demonstrate the speed and the accuracy of the proposed fast method.     

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.     

Lead field computation for the electrocardiographic inverse problem--finite elements versus boundary elements

In order to be able to solve the inverse problem of electrocardiography, the lead field matrix (transfer matrix) has to be calculated. The two methods applied for computing this matrix, which are compared in this study, are the boundary element method (BEM) and the finite element method (FEM). The performance of both methods using a spherical model was investigated. For a comparable discretization level, the BEM yields smaller relative errors compared to analytical solutions. The BEM needs less computation time, but a larger amount of memory. Inversely calculated myocardial activation times using either the FEM or BEM computed lead field matrices give similar activation time patterns. The FEM, however, is also capable of considering anisotropic conductivities. This property might have an impact for future development, when also individual myocardial fiber architecture can be considered in the inverse formulation.     

新的声纳图像自动分割方法

对水下声纳图像进行目标分割是非常复杂的,它不仅取决于被分割的不同目标,还与海底混响噪声、背景区域有着紧密的联系。通过分析声纳图像的特点,提出了一种新的声纳图像自动分割方法,即利用一种快速的模糊C均值聚类方法来完成初始分割,然后利用初始分割结果对马尔可夫模型的初始参数进行估计,最后,根据马尔可夫理论进行迭代条件估计,得到精确的图像分割结果。最后利用实测数据,验证了此种算法的可行性和有效性。