Boundary Element Method with Non-overlapping Domain Decomposition for Diffusion Equation

A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integration process always restarts from the initial time condition. The process of replacing the interface values, which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel iterative procedure. Numerical experiments demonstrate that the implementation of the present algorithm is efficient.

A Parallel Global-Local Mixed Evolutionary Algorithm for Multimodal Function Optimization Based on Domain Decomposition

This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.

ANALYSIS OF WAVEGUIDE PROBLEMS USING A RELAXED ITERATIVE DOMAIN DECOMPOSITION METHOD COMBINED WITH MULTIFRONTAL ALGORITHM

In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.

An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.

CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

In this paper,we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem.More precisely,we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions.Then we give a simple method to estimate the new value of parameters in each iteration.The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps.Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.

基于优化变分模态分解的混凝土浅层空洞病害识别

针对开放环境下混凝土空洞病害检测的病害特征识别中噪声干扰、成分识别问题进行了研究,提出了基于优化变分模态分解(improved variational mode decomposition,IVMD)与自由振动衰减速度的混凝土浅层病害声振信号识别方法。该研究建立了混凝土浅层空洞病害的理论模型,仿真了不同工况下的病害特征频率及其变化规律;提出了基于IVMD的信号分解方法,设计了基于Tent混沌与柯西变异优化的麻雀搜索算法联合搜索变分模态分解的关键参数k和α,在最佳分解的基础上提出了基于自相关函数图形、相关系数、衰减系数与频域分布情况的浅层空洞病害本征模态函数(intrinsic mode function,IMF)识别方法;选取幅值衰减评估了特征IMF的衰减速度,得出了基于振动衰减特征的空洞病害识别方法;通过预埋病害模型试验对比分析,验证了所提方法的有效性。研究结果表明,基于IVMD的分解方法能够有效降低噪声及其他成分的干扰,提高空洞病害识别精度和准确度。

基于PSO-SVM的Φ-OTDR系统模式识别研究

针对相位敏感光时域反射仪(phase sensitive optical time domain reflectometer,Φ-OTDR)系统中误报率高的问题,提出一种多域特征提取与粒子群算法优化支持向量机(particle swarm optimization-support vector machine,PSO-SVM)相结合的模式识别算法。首先,对原始信号进行差分处理后提取时域特征,并利用小波包分解方法,通过验证不同分解层数下的事件分类准确率,设定最优分解层数为6层,提取差分信号的能量特征。然后以SVM分类器为基础,利用PSO算法优化SVM分类器参数,提高光纤振动信号识别准确率。最后利用Φ-OTDR事件数据集进行验证,实验结果表明,该模式识别算法达到了95.6%的振动事件分类准确率。

各向异性问题的多子域区域分解算法

在自然边界归化原理的基础上,构造了一种无界凹角区域上各向异性问题的多子域非重叠区域分解算法,这是两子域的非重叠区域分解法的推广.本文给出了多子域区域分解算法的离散和变分形式,利用等价性理论,通过详细的理论证明说明此算法是收敛的,且与网格参数h无关.

高分辨率地震勘探数据的噪声抑制算法研究

近年来,随着地震勘探技术的发展,高分辨率地震勘探数据成为地震勘探的重要数据源,这些数据提供了更细致、更清晰的地下结构信息,对于提高资源勘探的精度和效率具有重要意义。然而,在地震数据处理过程中,不可避免地存在噪声,严重影响了地震数据的分辨率和准确性。因此,为获得高分辨率地震数据,噪声抑制的重要性显而易见。基于此,详细讨论各类噪声的特性,探讨当前主要噪声抑制算法,比较这些算法的性能,对提高高分辨率地震勘探数据的质量,进一步揭示地下复杂结构信息,提高地震勘探和资源勘查准确性具有重要意义。

基于EMD分解算法的长距离特高压输电线路接地故障定位

由于传统方法在长距离特高压输电线路接地故障定位中应用效果不佳,不仅定位结果相对误差较大,而且定位时间较长,无法达到预期的定位效果,因此提出基于EMD分解算法的长距离特高压输电线路接地故障定位。利用电压传感器采集输电线路电压信号,通过EMD分解算法对信号进行分解处理,提取信号时域特征,根据时域特征确定接地故障位置,以此实现基于EMD分解算法的长距离特高压输电线路接地故障定位。经实验证明,设计方法定位结果相对误差在2 m以内,定位用时在1 s以内,在长距离特高压输电线路接地故障定位方面具有良好的应用效果。

PARALLEL SCHWARZ ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES

In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of time-step and space-mesh. We prove that the, approximate solution has convergence independent of iteration times at each time-level. And the L^2 error estimates are given.

Some Massively Parallel Algorithms from Nature

We introduced the work on parallel problem solvers from physics and biology being developed by the research team at the State Key Laboratory of Software Engineering, Wuhan University. Results on parallel solvers include the following areas: Evolutionary algorithms based on imitating the evolution processes of nature for parallel problem solving, especially for parallel optimization and model-building; Asynchronous parallel algorithms based on domain decomposition which are inspired by physical analogies such as elastic relaxation process and annealing process, for scientific computations, especially for solving nonlinear mathematical physics problems. All these algorithms have the following common characteristics: inherent parallelism, self-adaptation and self-organization, because the basic ideas of these solvers are from imitating the natural evolutionary processes.

A MONOTONE DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS

This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.

THE ANALYSIS OF THE SEPARATED LAYERS ALGORITHM BY DOMAIN DECOMPOSITION METHOD

From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.

基于角域重采样与VMD的电梯曳引轮轴承故障诊断方法

针对曳引轮轴承故障诊断效果易受变转速工况和环境噪声影响的问题,提出了一种基于轿厢运行速度估计曳引轮转速的角域重采样方法,以及基于麻雀搜索算法(SSA)优化变分模态分解(VMD)参数的曳引轮轴承故障诊断方法。首先,采用轿厢运行速度估计曳引轮转速的方法,对曳引轮轴承振动信号进行了角域重采样;然后,采用SSA算法优化VMD参数的方法,对振动信号进行了分解,并根据最大峭度准则选取了分量,提取了曳引轮轴承故障特征指标;最后,搭建了电梯试验台,开展了故障注入试验,构建了多种分类模型,对基于角域重采样与SSA-VMD的曳引轮轴承故障诊断方法的有效性进行了验证。研究结果表明:曳引轮轴承角域重采样后的诊断效果明显优于未角域重采样的诊断效果,故障识别率提高了5%以上;实验条件下采用SSA-VMD方法能够准确地提取曳引轮轴承故障特征,故障识别率可达到95%。

Space-Time Decomposition of Kalman Filter

We present an innovative interpretation of Kalman filter(KF)combining the ideas of Schwarz domain decomposition(DD)and parallel in time(PinT)approaches.Thereafter we call it DD-KF.In contrast to standard DD approaches which are already incorporated in KF and other state estimation models,implementing a straightforward data parallelism inside the loop over time,DD-KF ab-initio partitions the whole model,including filter equations and dynamic model along both space and time directions/steps.As a consequence,we get local KFs reproducing the original filter at smaller dimensions on local domains.Also,sub problems could be solved in parallel.In order to enforce the matching of local solutions on overlapping regions,and then to achieve the same global solution of KF,local KFs are slightly modified by adding a correction term keeping track of contributions of adjacent subdomains to overlapping regions.Such a correction term balances localization errors along overlapping regions,acting as a regularization constraint on local solutions.Furthermore,such a localization excludes remote observations from each analyzed location improving the conditioning of the error covariance matrices.As dynamic model we consider shallow water equations which can be regarded a consistent tool to get a proof of concept of the reliability assessment of DD-KF in monitoring and forecasting of weather systems and ocean currents.

Splitting extrapolation based on domain decomposition for finite element approximations

Splitting extrapolation based on domain decomposition for finite element approximations is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem is turned to many discrete problems involving several grid parameters The multi-variate asymptotic expansions of finite element errors on independent grid parameters are proved for linear and nonlin ear second order elliptic equations as well as eigenvalue problems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method.

A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR EXTERIOR 3-D PROBLEM

Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Discussion of the discrete form of the D-N alternating algorithm.