Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continu...
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Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continuous mappings, and b ∈Rn a known vector. The establishments of these new methods are according to the principle of sufficiently using the delayed information and are concerning about the concrete characteristics of the multiprocessor systems. Therefore, they have considerably higher parallel computingefficiency. The global convergenge as well as the asymptotic convergence rates of these new methods are investigated in detail under suitable conditions.
In using the methods given by [1] to compute the hypersingular integrals on interval,one should select the mesh carefully in such a way that singular point falls near the center of a subinterval. A numerical method gi...
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In using the methods given by [1] to compute the hypersingular integrals on interval,one should select the mesh carefully in such a way that singular point falls near the center of a subinterval. A numerical method given in this paper might solve this problem. This new method is very simple, easy to be implemented, and above all, notaffected by the location of singular point.
In this paper the natural boundary reduction, suggested by Feng and Yu[1], is applied to deal with the three-dimensional problems. By expansion in spherical harmonics, we obtain the natural integral equations of harmo...
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In this paper the natural boundary reduction, suggested by Feng and Yu[1], is applied to deal with the three-dimensional problems. By expansion in spherical harmonics, we obtain the natural integral equations of harmonic problems over interior and exterior spherical domains. Meanwhile, we develop a numerical method for sloving these equations. Some numerical examples are also given to illustrate our method.
This paper deals with parallel implemeatation on distributed memory systemsof a pressure-correction projection scheme for the unsteady incompressible NavierStokes equations, the CNMT2 scheme (i.e., the Crank-Nickolson...
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This paper deals with parallel implemeatation on distributed memory systemsof a pressure-correction projection scheme for the unsteady incompressible NavierStokes equations, the CNMT2 scheme (i.e., the Crank-Nickolson Modified Temamscheme Ⅱ), presented in [1, 2]. The key point of this work is to study parallelizationof the fast Poisson solver [2] and analyse its parallel efficiency. Various techniques,such as pipelining and canon cyclic algorithm, were used to ensure good parallel performance and scalability of the algorithm. The algorithm has been implemented using MPI message passing environment and numerical tests have been carried out on various computers, including the home made Dawn-1000 MPP system and workstation clusters.
In this paper, based on the study of [1], the discretizations of the coupling of finite elemellt and boundary integral are presented to solve the initial boundary value problem of parabolic partial differential equati...
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In this paper, based on the study of [1], the discretizations of the coupling of finite elemellt and boundary integral are presented to solve the initial boundary value problem of parabolic partial differential equation defined on an unbounded *** semi-discrete scheme and fully discrete scheme are given, and stability theorem and error estimates, which correspond to discrete scheme respectively,are ***,the numerical example is provided,and numerical result shows that the method is feasible and effective.
Correction methods for the steady semi-periodic motion of incompressible fluid are investigated. The idea is similar to the influence matrix to solve the lack of vorticity boundary conditions. For any given boundary...
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Correction methods for the steady semi-periodic motion of incompressible
fluid are investigated. The idea is similar to the influence matrix to solve the
lack of vorticity boundary conditions. For any given boundary condition of the
vorticity, the coupled vorticity-stream function formulation is solved. Then solve
the governing equations with the correction boundary conditions to improve the
solution. These equations are numerically solved by Fourier series truncation and
finite difference method. The two numerical techniques are employed to treat the non-
linear terms. The first method for small Reynolds number R equals 0-50 has the same
results as that in M. Anwar and S.C.R. Dennis' report. The second one for R greater
than 50 obtains the reliable results. (Author abstract) 4 Refs.
Presents a study which applied the overlapping domain decomposition method based on the natural boundary reduction to solve the boundary value problem of harmonic equation over domain. Methods to solve boundary value ...
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Presents a study which applied the overlapping domain decomposition method based on the natural boundary reduction to solve the boundary value problem of harmonic equation over domain. Methods to solve boundary value problems; Contraction factor for the domain; Results.
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