Trace Averaging Domain Decomposition Method with Nonconforming Finite Elements

1.IntroductionDomaindec0mpositionreferstonumericaJmethodsf0robtainingsoluti0nsofsci-entificandengineeringproblemsbycombiningsoluti0nstoproblemspo8ed0nphysica1subdomains,or,moregeneraJly,byc0mbiningsoluti0nst0appropriatelyconstructedsubproblems.IthasbeenasubjectofintenseinterestreceDtlybecause0fitssultabil-ityforimplementationonhighperformancecomputerarchitectures.Somepapersarelistedinthereferencesherein,wlilchindicatethatmuchprogresshasbeenmadeinthestudyofnonoverlaPdomaindecompositionmethods…     

Hamilton-Jacobi-Bellman方程的区域分解算法

对离散Hamilton-Jacobi-Bellman方程提出了一类区域分解算法,并在合理的假设下证明了该算法的单调收敛性,数值结果表明该算法的有效性与准确性．     

Nonoverlapping Domain Decomposition Method with Mixed Element for Elliptic Problems

1.IntroductionDomaindecompositionasanewmethodofcomputationalmathematics,waJsdevel-opedsincethedevelopmentofparallelcomputersandmultiprocessorsupercomputers-Usingdomaindecompositionwecandecreasethescaleoftheproblemandimplementthesub-problemsonparallelcomputer.Fromatechnicalpointofviewmostofdo-maindecompositionmethodsconsideredsofarhavebeendealingwithfiniteelementmethods.In[1,2]ZhangandHuanghavegivenakindofnonoverlappingdomaindecompositionprocedurewithpiecewiselinearfiniteelementapproximation.…     

Stokes问题的区域分解法

本文主要讨论了Ｓｔｏｋｅｓ问题的非重迭型两仓区域性情形的区域分解算法，首先讨论了连续情形，然后将区域分解算法应用到Ｓｔｏｋｅｓ问题的非协调离散情形。     

关于非协调位移元与杂交应力元的对应性

本文阐明了E.L.Wilson[3]等的非协调移位元与卞学鐄的杂交应力元之间所存在的对应性.     

A Domain Decomposition Method for Frictional Contact Problem

The bilateral or unilateral contact problem with Coulomb friction between two elastic bodies is considered [1]. An algorithm is introduced to solve the resulting finite element system by a non‐overlapping domain decomposition method. The global problem is transformed to a smaller problem on the contact surface. The solution is obtained by using a successive approximation method, in each step of this algorithm we solve two intermediate problems the first with prescribed tangential pressure and the second with prescribed normal pressure.     

Non-overlapping Domain Decomposition Method for a Nodal Finite Element Method

A new approach is proposed for constructing nonoverlapping domain decomposition procedures for solving a linear system related to a nodal finite element method. It applies to problems involving either positive semi-definite or complex indefinite local matrices. The main feature of the method is to preserve the continuity requirements on the unknowns and the finite element equations at the nodes shared by more than two subdomains and to suitably augment the local matrices. We prove that the corresponding algorithm can be seen as a converging iterative method for solving the finite element system and that it cannot break down. Each iteration is obtained by solving uncoupled local finite element systems posed in each subdomain and, in contrast to a strict domain decomposition method, is completed by solving a linear system whose unknowns are the degrees of freedom attached to the above special nodes.     

空间半无界区域的非重叠区域分解算法

主要研究了空间一种半无界凹球区域上的区域分解算法.在三维空间自然边界规划的基础上,以三维Dirichlet外边值问题为例,进行的D-N交替算法.并提出了该算法与Richardson迭代法的等价性,并分析其收敛性及其收敛速度与网格参数h无关.同时给出了松弛因子的取值范围.     

Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization

We concern with fast domain decomposition methods for solving the total variation minimization problems in image processing. By decomposing the image domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and subdomain problems are uniformly convex, we can apply the acceleration method to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing methods are discussed, which not only demonstrate the advantages of our method but also support the theoretical convergence rate.     

基于对称化原理的对称区域分裂法

本文利用对称化原理,讨论了一种只需在子区域上计算两个完全独立子问题就可得到原问题解的对称区域分裂法,并用此方法求解线性算子方程和线性透射问题.此方法可作为并行算法在MIMD计算机上使用.     

无穷凹角区域各向异性问题的重叠型区域分解算法

本文以凹角椭圆外区域上调和问题的自然边界归化为基础,提出了求解无穷凹角区域各向异性问题的重叠型区域分解算法,并分析了算法的收敛性及收敛速度.最后给出了数值例子,以示方法的可行性和有效性.     

一元四次整系数多项式的因式分解法

仅对一元四次整系数多项式在实数域内分解问题进行了研究,根据分解后其系数应为二次代数整数的特点,以及导出的二次方程判别式的完全平方性质,得出了一元四次整系数多项式在实数域内能分解成两个二次因式乘积的条件及方法,从而解决了一元四次整系数多项式在实数域内的因式分解问题.     

Multigrid Multi-Level Domain Decomposition

The domain decomposition method in this paper is based on PCG (Preconditioned Conjugate Gradient method). If $N$ is the number of subdomains, the number of sub-problems solved parallelly in a PCG step is $\frac{4}{3}(1-\frac{1}{4^{\log N+1}})N$. The condition number of the preconditioned system does not exceed $O(1+\log N)^3$. It is completely independent of the mesh size. The number of iterations required, to decrease the energy norm of the error by a fixed factor, is proportional to $O(1+\log N)^{\frac{3}{2}}$ .     

The Optimal Preconditioning in the Domain Decomposition Method for Wilson Element

1.TheCollstructionofPreconditionerLetfil)eapolygolldolllaillillR',feL'(fl).Consi(lertheholllogeneousDiricllletboulldaryvalueProblenlofPoissonequation,Assllmethat,fordomainfi,thereareacoarsersubdivisionTHwitllIneshsizeHalldananotheroneThwithmeshsizeh,whichisobtainedbyrefiningTH'Thebotllsubdivisionssatisfythequasi-uniformityandtheillversehypothesis.FOragivenelemelltT,Pm(T)dellotesthespaceofallpolynomialswiththedegreenotgreaterthanm,Qm(T)denotesthespaceofallpolynomialswiththedegreecorres…     

DD‐type Domain Decomposition Method for Frictional Contact Problem

The bilateral or unilateral contact problem with Coulomb friction between two elastic bodies is considered [1]. An algorithm is introduced to solve the resulting finite element system by a non‐overlapping domain decomposition method. The global problem is transformed to a smaller problem on the contact surface. The solution is obtained by using a successive approximation method, in each step of this algorithm we solve two intermediate problems the first with prescribed tangential pressure and the second with prescribed normal pressure.     

Partitioned-GMRES in Domain Decomposition with Approximate Subdomain Solution

Solution of large linear systems encountered in computational fluid dynamics often leads to some form of domain decomposition, especially when it is desired to use parallel machines. In this paper P-GMRES, a partitioned modification of GMRES, is applied to such problems. It is shown that P-GMRES converges faster than GMRES if the subdomains are solved exactly, and that P-GMRES requires less communication in the computation of the inner products. Also, approximate solutions for the subdomains by an inner preconditioned GMRES iteration are considered, in combination with a restarted version of P-GMRES. It turns out that rather crude tolerances are allowed, and that a good strategy is to vary the tolerance for the subdomains in the course of the outer iteration.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.     

A Robin-Robin Domain Decomposition Method for a Stokes-Darcy Structure Interaction with a Locally Modified Mesh

A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow. The fluid flow is modeled by the Stokes equations while the porous media flow is modeled by Darcy's law. The method is based on a Robin-Robin domain decomposition method with a Cartesian mesh with local modifications near the interface. Some computational examples are presented and discussed.     

关于并行迭代区域分解算法收敛性的注记

本文给出在范数Ⅱ·Ⅱ下的收敛估计,以及相应的最优松驰因子,还讨论了这两种收敛性之间的关系.     

Dynamical Particle Simulation with Parallel Cache-Aware Domain Decomposition Strategies

The simulation of large particle systems with the Discrete Element Method can be very time consuming. This is due to the necessity for collision detection between the disordered particles. Various methods, originating from different areas such as computer science, are well established and have been used in various applications. For parallel computations the simulation domain needs to be divided into subdomains to be distributed among the different nodes or machines within a supercomputer or a computer-cluster. The strategy for this domain decomposition has a significant influence on the performance of the calculation. In this paper we discuss some aspects of the development of a hierarchical domain decomposition algorithm that provides flexible adaption of the decomposition pattern to the changing structure of the particle system during the simulation. Thus an even load distribution among the different machines can be maintained. Moreover, the same method is also used to deal with the computational bottleneck caused by the presence of unstructured data. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)