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, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is b...
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In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity, defined respectively on a coarse grid with grids size H and another fine grid with grid size h<< H, a finite element space Mh for the approximation of the pressure and two finite element spaces AH and Wh, for the approximation of the temperature,also defined respectivply on the coarse grid with grid size H and another fine grid with grid size h. The existence and the convergence of the fully discrete mixed element solution are shown. The scheme consists in using standard backward one step Euler-Galerkin fully discrete format at first L0 steps (L0 2) on fine grid with grid size h, but using nonlinear Galerkin mixed element method of backward one step Euler-Galerkin fully discrete format through L0 + 1 step to end step. We have proved that the fully discrete nonlinear Galerkin mixed element procedure with respect to the coarse grid spaces with grid size H holds superconvergence.
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.
In this paper, a nonlinear Galerkin (semi-discrete) mixed element method for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approxima...
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In this paper, a nonlinear Galerkin (semi-discrete) mixed element method for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity,defined respectively on a coarse grid with grid size H and another fine grid with grid size h << H, a finite element space Mh for the approximation of the pressuxe and two finite element spaces WH and Wh for the approximation of the temperature,also defined respectively on the coarse grid with grid size H and another fine grid with grid size h << H. Both of the non linearity and time dependence are treated only in the coarse space. We have proved that the error between the nonlinear Galerkin mixed element solution and standard Galerkin mixed element solutionis of the order of Hm+1(m>1), all in velocity (H1(Ω)2 norm), pressure (L2(Ω)norm) and temperature (H1 (Ω) norm).
This paper presents a class of high resolution KFVS (kinetic flux vector split-ting) finite volum methods for solving three-dimensional compressible Euler equa-tions with γ-gas law. The schemes are obtained based on ...
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This paper presents a class of high resolution KFVS (kinetic flux vector split-ting) finite volum methods for solving three-dimensional compressible Euler equa-tions with γ-gas law. The schemes are obtained based on the important connection between the Boltzmann equation and the Euler equations. According to the sign of the normal molecular velocity component at the surface of ally control volumes,one gives a splitting of the macroscopic flux vector, i.e. writes the macroscopic flux vector into the sum form of a positive flux and a negative flux. The initial reconstruction is applied to improve resolution of the schemes. Several numerical results are also presented to show the performance of our schemes.
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