Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary

Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.     

基于加性算子分割的快速静磁场主动轮廓模型

针对静磁力主动轮廓模型计算复杂度较高,收敛速度较慢的问题。将该模型对应的水平集方程做隐式数值化,采用加性算子分割方法（AOS）求解。实验发现,这种改进后的静磁场主动轮廓模型不仅保留了原有模型的优点,而且提高原有模型的收敛速度和稳定性。     

Boundary element methods for magnetostatic field problems: a critical view

For the solution of magnetostatic field problems we discuss and compare several boundary integral formulations with respect to their accuracy, their efficiency, and their robustness. We provide fast boundary element methods which are able to deal with multiple connected computational domains, with large magnetic permeabilities, and with complicated structures with small gaps. The numerical comparison is based on several examples, including a controllable reactor as a real-world problem.     

Coupling projection domain decomposition method and Kansa's method in electrostatic problems

This paper present a novel approach for solving electrostatic problems associated with an asymmetrical shielded stripline and shielded coupled-striplines. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method (also, Kansa's method) with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincaré interface equation and the original problem is solved by computing a series of independent subproblems. Two real problems are solved by the proposed approach to demonstrate the accuracy and efficiency.     

Parallel implementation of fast multipole method based on JASMIN

Fast multipole method (FMM) may reduce the complexity of N-body problems from O(N 2 ) to O(N log N) or O(N).It was applied in problems ranging from electromagnetic scattering to dislocation dynamics.FMM can be divided into two parts: commonness and individuality.A parallel solver of FMM commonly used in various applications has been designed and implemented in JASMIN infrastructure.The solver encapsulates the commonness.Furthermore,it supplies users with abstract interfaces required to implement the individ...     

Fast parallel solution of boundary integral equations and related problems

This article is concerned with the efficient numerical solution of Fredholm integral equations on a parallel computer with shared or distributed memory. Parallel algorithms for both, the approximation of the discrete operator by hierarchical matrices using adaptive cross approximation (ACA) and the parallel matrix-vector multiplication of such matrices by a vector, are presented. The first algorithm has a complexity of order p ^-1 N log^2d-1 N, while the latter is of order p ^-1 N log ^d N, where N, d and p are the number of unknowns, the spatial dimension and the number of processors, respectively. The approximant needs Ω(p ^-1 N log ^d N) units of storage on each processor. Dedicated to George C. Hsiao on the occasion of his 70th birthday. Mathematics Subject Classification (2000)65D05 65D15 65F05 65F30 Communicated by: U. Langer     

Parallel computation of three-dimensional nonlinear magnetostatic problems

We describe a general-purpose parallel code for computing accurate solutions to large computationally demanding, 3D, nonlinear magnetostatic problems. The code, CORAL, is based on a volume integral equation formulation. Using an IBM SP parallel computer and iterative solution methods, we successfully solved the dense linear systems inherent in such formulations. A key component of our work was the use of the PETSc library, which provides parallel portability and access to the latest linear algebra solution technology. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Finite-difference vector-potential solution of transient electromagnetic field problems

A finite-difference time–space numerical algorithm for the analysis of transient electromagnetic fields is proposed based on the expression of the field vectors in terms of vector potential functions. The method allows for both integral and finite-difference calculation of the potential functions (PF). Both approaches can be applied in combination. Since it is based on the time-domain integral-equation approach, it reduces the 3D problem to a 2D one, and only the tangential vector potential components are involved in the calculation. The consistency of the method has been proved by simulations of Gaussian pulse propagation in a homogeneous and an open-end microstripline and a thin-plate scattering problem. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 56–67, 1998.     

Fast support-based clustering method for large-scale problems

In many support vector-based clustering algorithms, a key computational bottleneck is the cluster labeling time of each data point which restricts the scalability of the method. In this paper, we review a general framework of support vector-based clustering using dynamical system and propose a novel method to speed up labeling time which is log-linear to the size of data. We also give theoretical background of the proposed method. Various large-scale benchmark results are provided to show the effectiveness and efficiency of the proposed method.     

A solution method for dynamic contact problems

An efficient method is presented for analyzing the transient dynamic contact problems of elastic bodies in this paper. This approach exploits the Lagrange multiplier concept and a special time integration algorithm. Due to the introduced high-frequency dissipation in this time integration algorithm, this method can lead to the effective analysis of real response of elastic bodies with dynamic surface contact constraints. The results of numerical examples show that this method can avoid the weakness of the classical Lagrange multiplier method in dealing with dynamic contact problems with relatively high inertial forces. Stable results can be provided when the time integration step size is small. The properties of this method have also been discussed in this paper.     

Parallel solution of contact shape optimization problems based on Total FETI domain decomposition method

An application of a variant of the parallel domain decomposition method that we call Total FETI or TFETI (Total Finite Element Tearing and Interconnecting) for the solution of contact problems of elasticity to the parallel solution of contact shape optimization problems is described. A unique feature of the TFETI algorithm is its capability to solve large contact problems with optimal, i.e., asymptotically linear complexity. We show that the algorithm is even more efficient for the solution of the contact shape optimization problems as it can exploit effectively a specific structure of the auxiliary problems arising in the semi-analytic sensitivity analysis. Thus the triangular factorizations of the stiffness matrices of the subdomains are carried out in parallel only once for each design step, the evaluation of the components of the gradient of the cost function can be carried out in parallel, and even the evaluation of each component of the gradient itself can be further parallelized using the standard TFETI scheme. Theoretical results which prove asymptotically linear complexity of the solution are reported and documented by numerical experiments. The results of numerical solution of a 3D contact shape optimization problem confirm the high degree of parallelism of the algorithm.     

基于NCC的快速匹配算法

景象匹配在地形辅助导航中具有十分重要的地位,归一化互相关(NCC)技术是一种相对抗噪声能力强、匹配准确的匹配算法,因此,在导航制导中广泛应用。但由于其运算量比较大,对于要求实时匹配的地形辅助导航系统来说,其运算速度需要进一步提高。在NCC方法的基础上,把卷积用于景象匹配,大大简化并提高了NCC的匹配速度。仿真实验证明了此方法的快速性和有效性。     

一种基于独立任务的POMDP问题的解决方法*

部分可观测马尔可夫决策过程(POMDP)是马尔可夫决策过程(MDP)的扩展。通常利用POMDPs来模拟在部分可观测的随机环境中决策的Agents。针对完整POMDP的求解方法扩展能力弱的问题,提出把一个多元的POMDP分解成一组受限制的POMDPs,然后分别独立地求解每个这样的模型,获得一个值函数并将这些受限制的POMDPs的值函数结合起来以便获得一个完整POMDP的策略。该方法主要阐述了识别与独立任务相关的状态变量的过程,以及如何构造一个被限制在一个单独任务上的模型。将该方法应用到两个不同规模的岩石采样问题中,实验结果表明,该方法能够获得很好的策略。     

基于快速多极边界元法的沥青混凝土弹性模量预测

由于对沥青混凝土材料的研究无论是试验法还是经验法均建立在宏观层面上,无法与其细观结构建立本质的联系,因此利用快速多极边界元法(Fast Multipole Boundary Element Method,FMBEM),结合数字图像处理技术,实现沥青混凝土二维几何建模及弹性模量预测.通过数字图像处理技术识别拍摄得到的原始...     

Total-FETI domain decomposition method for solution of elasto-plastic problems

In this paper we present an algorithm for the parallel solution of the rate-independent elasto-plastic problems with kinematic hardening. We assume the von Mises plastic criterion and the associated plastic flow rule. The time discretization is based on the implicit Euler method. The corresponding one-time-step problem is formulated in the incremental form with respect to the unknown displacement and discretized spatially by the finite element method. We use an ‘external’ algorithm based on a linearization of the elasto-plastic stress–strain relation by the corresponding tangential operator and we parallelize the arising linearized problem by the Total-FETI method. The numerical experiments were carried out using our novel C/C++ library FLLOP (FETI Light Layer On top of PETSc) at HECToR supercomputer located at EPCC, UK.     

A two-level iteration method for solution of contact problems

The merits and limitations of some existing procedures for the solution of contact problems, modeled by the finite element method, are examined. Based on the Lagrangian multiplier method, a partitioning scheme can be used to obtain a small system of equation for the Lagrange multipliers which is then solved by the conjugate gradient method. A two-level contact algorithm is employed which first linearizes the nonlinear contact problem to obtain a linear contact problem that is in turn solved by the Newton method. The performance of the algorithm compared to some existing procedures is demonstrated on some test problems.