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ANALYSIS OF WAVEGUIDE PROBLEMS USING A RELAXED ITERATIVE DOMAIN DECOMPOSITION METHOD COMBINED WITH MULTIFRONTAL ALGORITHM 认领 引用 被引量：1
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作者 Zhu Hanqing Wu Zhengde K. M. Luk 《Journal of Electronics(China)》 2003年第2期110-115,共6页
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 t... 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. 展开更多
关键词 Fictitious boundary condition Domain decomposition method Relaxed algorithm Multifrontal algorithm Waveguide problem
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An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations 认领 引用 被引量：1
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作者 Liyong Zhu Guangwei Yuan Qiang Du 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第3期301-325,共25页
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 ... 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. 展开更多
关键词 Convection diffusion equation parallel algorithm domain decomposition modifiedupwind differences predictor-corrector explicit-implicit scheme convergence analysis.
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Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation 认领 引用
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作者 尚月强 何银年 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第9期1177-1182,共6页
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 add... 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. 展开更多
关键词 domain decomposition algorithm Schwarz method Fourier transform biharmonic equation
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Eddy Current Analyses by Domain Decomposition Method Using Double-Double Precision 认领 引用
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作者 Mizuma Takehito Takei Amane 《Computer Modeling in Engineering & Sciences》 SCIE EI 2018年第9期349-363,共15页
A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative met... A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results. 展开更多
关键词 Double-double precision domain decomposition method eddy current analysis parallel finite element method
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A HYBRID TWO-LEVEL FINITE ELEMENT METHOD FOR THE STATIONARY NATURAL CONVECTION PROBLEM AND PARALLEL IMPLEMENT 认领 引用
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作者 Guoliang Zhang Hongtao Chen +1 位作者 Qiaoling He Jingwei Li 《Journal of Computational Mathematics》 SCIE CSCD 2026年第6期1848-1866,共19页
This study presents a novel hybrid approach for addressing incompressible stationary natural convection problem,incorporating a parallel technique to enhance computational efficiency.Inspired by the traditional two-le... This study presents a novel hybrid approach for addressing incompressible stationary natural convection problem,incorporating a parallel technique to enhance computational efficiency.Inspired by the traditional two-level method[He and Wang,Comput.Methods Appl.Mech.Engrg.,197(2008)]and the two-step approach[Wu et al.,Int.J.Heat Mass Transfer,101(2016)],both characterized by their iterative and corrective processes,we endeavor to alleviate the computational burden associated with the iterative process.Building upon these methods,our novel hybrid method involves two primary steps:initially solving the original problem using the finite element pair P1 b-P1-P1 on a coarse mesh,followed by resolving the linearized equations using the higher-order pair P2-P1-P2 on a fine mesh.While the first step employs iterative techniques,the second step entails directly solving a linearized problem.This novel approach can save lots of computational time in the iterative step compared to the traditional methods.Moreover,leveraging domain decomposition techniques,we implement a parallel strategy to further accelerate computations.Finally,we conduct several numerical examples to validate the efficiency of the proposed algorithms.The numerical results demonstrate optimal convergence rates comparable to those obtained using only the P2-P1-P2 finite element pair under similar relative error conditions.Furthermore,the numerical simulations on the two obstacles flow and Bénard convection problem show the robustness and efficiency of the proposed algorithms. 展开更多
关键词 Natural Convection Problem Finite Element Method Hybrid Two-Level Method Parallel Algorithm Fully Overlapping Domain Decomposition
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THE ANALYSIS OF THE SEPARATED LAYERS ALGORITHM BY DOMAIN DECOMPOSITION METHOD 认领 引用
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作者 He Zi-gan , Sun Chuan-hongDalian University of Technology, Dalian 116023, P. R. China 《Journal of Hydrodynamics》 SCIE EI 1994年第3期64-69,共6页
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 propertie... 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. 展开更多
关键词 domain decomposition method . separated- layers algorithm convergence linear partial differential equation.
Fast parallel factor decomposition technique for coherently distributed source localization 认领 引用 被引量：2
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作者 CHENG Qianlin ZHANG Xiaofei CAO Renzheng 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2018年第4期667-675,共9页
This paper links parallel factor（PARAFAC） analysis to the problem of nominal direction-of-arrival（DOA） estimation for coherently distributed（CD） sources and proposes a fast PARAFACbased algorithm by establishing... This paper links parallel factor（PARAFAC） analysis to the problem of nominal direction-of-arrival（DOA） estimation for coherently distributed（CD） sources and proposes a fast PARAFACbased algorithm by establishing the trilinear PARAFAC model.Relying on the uniqueness of the low-rank three-way array decomposition and the trilinear alternating least squares regression, the proposed algorithm achieves nominal DOA estimation and outperforms the conventional estimation of signal parameter via rotational technique CD（ESPRIT-CD） and propagator method CD（PM-CD）methods in terms of estimation accuracy. Furthermore, by means of the initialization via the propagator method, this paper accelerates the convergence procedure of the proposed algorithm with no estimation performance degradation. In addition, the proposed algorithm can be directly applied to the multiple-source scenario,where sources have different angular distribution shapes. Numerical simulation results corroborate the effectiveness and superiority of the proposed fast PARAFAC-based algorithm. 展开更多
关键词 source localization coherently distributed （CD）source parallel factor analysis propagator method （PM） trilin-ear decomposition
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A parallel two-level finite element method for the Navier-Stokes equations 认领 引用 被引量：2
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作者 尚月强 罗振东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第11期1429-1438,共10页
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations... Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method. 展开更多
关键词 Navier-Stokes equations finite element two-level method overlapping domain decomposition parallel algorithm
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Some Massively Parallel Algorithms from Nature 认领 引用
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作者 Li Yan Kang Li-shan +3 位作者 Chen Yu-ping Liu Pu Cao Hong-qing Pan Zheng-jun 《Wuhan University Journal of Natural Sciences》 EI CAS 2002年第1期37-46,共10页
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... 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. 展开更多
关键词 evolutionary computation parallel algorithm imitating nature domain decomposition knowledge discovery in databases
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A Distributed Newton Method for Processing Signals Defined on the Large-Scale Networks 认领 引用 被引量：1
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作者 Yanhai Zhang Junzheng Jiang +1 位作者 Haitao Wang Mou Ma 《China Communications》 SCIE CSCD 2023年第5期315-329,共15页
In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously pe... In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm. 展开更多
关键词 graph signal processing distributed Newton method active network decomposition secondorder algorithm
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Non-Iterative Parallel Schwarz Domain Decomposition Algorithms for a Two-Domain Parabolic Problem 认领 引用
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作者 Minjie Shen Danping Yang Haibiao Zheng 《Communications in Computational Physics》 SCIE CSCD 2025年第10期1552-1584,共33页
Based on overlapping domain decomposition,two parallel Schwarz finite element algorithms are presented for solving a two-domain parabolic problem.Our algorithms are based on two ideas.One is the observation that the i... Based on overlapping domain decomposition,two parallel Schwarz finite element algorithms are presented for solving a two-domain parabolic problem.Our algorithms are based on two ideas.One is the observation that the influence of the non-homogeneous boundary data diminishes exponentially towards the interior of the subdomains.Another is to apply proper partitions of unity to distribute the residuals of the discretized systems reasonably into many subdomains so as to avoid repeated correction in the overlapping parts.The resulting algorithms are fully parallel in each subdomain.At each time step,only one iteration step is required to reach the optimal order of accuracy.The convergence rate depending on the mesh parameters are analyzed.Finally,numerical results are reported,which verify the theoretical analysis. 展开更多
关键词 Domain decomposition parallel Schwarz method parabolic problems error estimate
PARALLEL SCHWARZ ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES 认领 引用
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作者 芮洪兴 羊丹平 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1997年第1期45-56,共12页
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 ti... 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. 展开更多
关键词 Schwarz algorithms parabolic equations domain decomposition error estimates parallel algorithm.
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AN OVERLAPPING DOMAIN DECOMPOSITION SPLITTING ALGORITHM FOR STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION 认领 引用
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作者 Lihai Ji 《Journal of Computational Mathematics》 SCIE CSCD 2025年第4期791-812,共22页
A novel overlapping domain decomposition splitting algorithm based on a CrankNicolson method is developed for the stochastic nonlinear Schrödinger equation driven by a multiplicative noise with non-periodic bound... A novel overlapping domain decomposition splitting algorithm based on a CrankNicolson method is developed for the stochastic nonlinear Schrödinger equation driven by a multiplicative noise with non-periodic boundary conditions.The proposed algorithm can significantly reduce the computational cost while maintaining the similar conservation laws.Numerical experiments are dedicated to illustrating the capability of the algorithm for different spatial dimensions,as well as the various initial conditions.In particular,we compare the performance of the overlapping domain decomposition splitting algorithm with the stochastic multi-symplectic method in[S.Jiang et al.,Commun.Comput.Phys.,14(2013),393-411]and the finite difference splitting scheme in[J.Cui et al.,J.Differ.Equ.,266(2019),5625-5663].We observe that our proposed algorithm has excellent computational efficiency and is highly competitive.It provides a useful tool for solving stochastic partial differential equations. 展开更多
关键词 Stochastic nonlinear Schrödinger equation Domain decomposition method Operator splitting Overlapping domain decomposition splitting algorithm
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A DISTRIBUTED LATTICE BOLTZMANN METHOD 认领 引用
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作者 Juhua Chen & Yuanxiang Li 《Wuhan University Journal of Natural Sciences》 CAS 1996年第Z1期442-445,共4页
In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the distri... In this paper, an overlapping lattice Boltzmann model is introduced and its domain decomposition method, a distributed lattice Boltzmann method is presented. Parallel effectiveness of some programs based on the distributed lattice Boltzmann method are analyzed. 展开更多
关键词 Lattice Boltzmann Method Domain Decomposition Method, Distributed Parallel Algorithm
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CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS 认领 引用 被引量：1
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作者 Minh-Phuong TRAN Thanh-Nhan NGUYEN +3 位作者 Phuoc-Toan HUYNH Nhu-Binh LY Minh-Dang NGUYEN Quoc-Anh HO 《Acta Mathematica Scientia》 SCIE CSCD 2022年第1期105-126,共22页
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 precis... 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. 展开更多
关键词 domain decomposition method Schwarz waveform relaxation algorithm advection reaction diffusion changing transmission conditions
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An Approach of Distributed Joint Optimization for Cluster-based Wireless Sensor Networks 认领 引用 被引量：13
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作者 Zhixin Liu Yazhou Yuan +1 位作者 Xinping Guan Xinbin Li 《IEEE/CAA Journal of Automatica Sinica》 EI 2015年第3期267-273,共7页
Wireless sensor networks (WSNs) are energyconstrained, so energy saving is one of the most important issues in typical applications. The clustered WSN topology is considered in this paper. To achieve the balance of en... Wireless sensor networks (WSNs) are energyconstrained, so energy saving is one of the most important issues in typical applications. The clustered WSN topology is considered in this paper. To achieve the balance of energy consumption and utility of network resources, we explicitly model and factor the effect of power and rate. A novel joint optimization model is proposed with the protection for cluster head. By the mean of a choice of two appropriate sub-utility functions, the distributed iterative algorithm is obtained. The convergence of the proposed iterative algorithm is proved analytically. We consider general dual decomposition method to realize variable separation and distributed computation, which is practical in large-scale sensor networks. Numerical results show that the proposed joint optimal algorithm converges to the optimal power allocation and rate transmission, and validate the performance in terms of prolonging of network lifetime and improvement of throughput. © 2014 Chinese Association of Automation. 展开更多
关键词 Algorithms Distributed computer systems Energy conservation Energy utilization Iterative methods Optimization Parallel algorithms Power control
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A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS 认领 引用 被引量：2
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作者 Dao-qi Yang 《Journal of Computational Mathematics》 SCIE EI 1998年第2期141-151,共11页
An iterative nonoverlapping domain decomposition procedure is proposed and analyzed for linear elliptic problems. At the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it ... An iterative nonoverlapping domain decomposition procedure is proposed and analyzed for linear elliptic problems. At the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. This procedure is suitable for parallel processing. A convergence analysis is established. Standard and mixed finite element methods are employed to give discrete versions of this domain decomposition algorithm. Numerical experiments arc conducted to show the effectiveness of the method. 展开更多
关键词 Domain decomposition methods finite element methods parallel computing
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高可扩展三维海洋可控源电磁高阶时域有限差分数值模拟 认领 引用
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作者 彭桦 吴志强 +5 位作者 肖调杰 李世杰 龚春叶 杨博 王浩东 陈星佑 《计算机工程与科学》 CSCD 北大核心 2026年第3期422-433,共12页
海洋可控源电磁法MCSEM广泛应用于水下目标电磁探测、海洋电磁通信和海洋油气资源勘探等领域。然而,当前MCSEM数值模拟面临计算精度不足、并行通信效率低下和扩展性受限等问题,难以满足大规模三维复杂模型的计算需求。为此,设计并实现... 海洋可控源电磁法MCSEM广泛应用于水下目标电磁探测、海洋电磁通信和海洋油气资源勘探等领域。然而,当前MCSEM数值模拟面临计算精度不足、并行通信效率低下和扩展性受限等问题,难以满足大规模三维复杂模型的计算需求。为此,设计并实现了一种基于四阶时域有限差分的多层级并行数值模拟算法。该算法采用发射源间并行计算和子区域并行求解策略,充分挖掘了并行粒度,并通过远程内存访问技术有效降低通信开销,显著提升了并行效率。然后,通过多个典型案例测试验证了该算法的正确性与高效性。结果表明,在发射源数量为8个、区域规模为20 km×20 km×12 km且网格规模为245×245×512情况下,针对不考虑空气层的深海模型,采用8个进程组共2048个进程时,计算时间由串行的57.05 h缩短至72.96 s,加速比超线性达到2815.04,并行效率为137.45%;针对考虑空气层的浅海模型,采用8个进程组共256个进程时,计算时间由串行的64.78 h缩短至59.75 min,加速比为65.05,并行效率为25.41%,表明所提算法具有较好的可扩展性及计算精度,为海洋电磁数值模拟提供了一种高效的解决方案。 展开更多
关键词 海洋可控源电磁 高阶时域有限差分方法 高性能计算 远程内存访问 并行算法 单侧通信
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High performance parallel computing of large eddy simulation of the flow in a curved duct with square cross section 认领 引用
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作者 樊洪明 黄伟 魏英杰 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第4期442-446,共5页
Large eddy simulation(LES) cooperated with a high performance parallel computing method is applied to simulate the flow in a curved duct with square cross section in the paper. The method consists of parallel domain d... Large eddy simulation(LES) cooperated with a high performance parallel computing method is applied to simulate the flow in a curved duct with square cross section in the paper. The method consists of parallel domain decomposition of grids, creation of virtual diagonal bordered matrix, assembling of boundary matrix, parallel LDL^T decomposition, parallel solving of Poisson Equation, parallel estimation of convergence and so on. The parallel computing method can solve the problems that are difficult to solve using traditional serial computing. Furthermore, existing microcomputers can be fully used to resolve some large-scale problems of complex turbulent flow. 展开更多
关键词 turbulent flow large eddy simulation finite element method domain decomposition method parallel computing
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Parallel programming characteristics of a DSP-based parallel system 认领 引用 被引量：1
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作者 GAO Shu GUO Qing-ping 《Journal of Zhejiang University-SCIENCE A》 EI CAS 2006年第10期1669-1675,共7页
This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming charact... This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming characteristics, especially the mode of communication, discussing how to design parallel algorithms and presenting a domain-decomposition-based complete multi-grid parallel algorithm with virtual boundary forecast (VBF) to solve a lot of large-scale and complicated heat problems. In the end, Mandelbrot Set and a non-linear heat transfer equation of ceramic/metal composite material are taken as examples to illustrate the implementation of the proposed algorithm. The results showed that the solutions are highly efficient and have linear speedup. 展开更多
关键词 Parallel algorithm Multi-grid Domain decomposition Virtual boundary forecast （VBF） DSP-based parallel system
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