THE CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stability and convergence of this new scheme.     

THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 < p < 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.     

FOURIER PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORICITY EQUATION

ＦＯＵＲＩＥＲＰＳＥＵＤＯＳＰＥＣＴＲＡＬ－ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＭＥＴＨＯＤＦＯＲＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＩＣＩＴＹＥＱＵＡＴＩＯＮ￥ＧＵＯＢＥＮＹＵ；ＸＩＯＮＧＹＵＥＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

THE ERRORS ESTIMATION OF THE CHEBYSHEV SPECTRAL－DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORTICITY EQUATION

ＴＨＥ　ＥＲＲＯＲＳ　ＥＳＴＩＭＡＴＩＯＮ　ＯＦ　ＴＨＥ　ＣＨＥＢＹＳＨＥＶ　ＳＰＥＣＴＲＡＬ－ＤＩＦＦＥＲＥＮＣＥ　ＭＥＴＨＯＤ　ＦＯＲ　ＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬ　ＶＯＲＴＩＣＩＴＹ　ＥＱＵＡＴＩＯＮＴＨＥＥＲＲＯＲＳＥＳＴＩＭＡＴＩＯＮＯＦ...     

FOURIER－CHEBYSHEV SPECTRAL METHOD FOR SOLVING THREE－DIMENSIONAL VORTICITY EQUATION

ＦＯＵＲＩＥＲ－ＣＨＥＢＹＳＨＥＶＳＰＥＣＴＲＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＴＩＣＩＴＹＥＱＵＡＴＩＯＮＧＵＯＢＥＮＹＵ（郭本瑜）；ＬＩＪＩＡＮ（李健）；ＭＡＨＥＰＩＮＧ（马和平）（Ｄｅｐａｒｔｍｅｎｔｏ...     

DOMAIN DECOMPOSITION METHOD FOR PARABOLIC EQUATION ON GENERAL DOMAIN

The nonoxerlapping domain deoomposition method for parabolic partial differential equation on general domain is considered. A kind of domain decomposition that uses the finite element procedure ks given. The problem.over the domains can be implemented on parallel computer. Convergence analysis is also presented.     

SCHWARZ DOMAIN DECOMPOSITION ALGORITHMS FOR BOUNDARY ELEMENT METHOD

In this paper, we introduce two Schwarz type domain decomposition algorithms for solving boundary element equations, which decompose the original problem defined on global boundary surface into several ones defined on sub-domains so that they may be solved ileratively or parallelly. The convergence of these methods are also proved.     

ON THE hp FINITE ELEMENT METHOD FOR THE ONE DIMENSIONAL SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS

In this work, a singularly perturbed two-point boundary value problem of convection-diffusion type is considered. An hp version finite element method on a strongly graded piecewise uniform mesh of Shishkin type is used to solve the model problem. With the analytic assumption of the input data, it is shown that the method converges exponentially and the convergence is uniformly valid with respect to the singular perturbation parameter.     

GLOBAL SHOCK SOLUTIONS TO A CLASS OF PISTON PROBLEMS FOR THE SYSTEM OF ONE DIMENSIONAL ISENTROPIC FLOW

The autors apply the result obtained in [1] to consider a class of discontinuous piston problems for the system of one dimensional isentropic flow and prove that this problem admits a unique global classical discontinuous solution only containing one shock.     

ASYMPTOTIC LIMITS OF ONE－DIMENSIONAL HYDRODYNAMIC MODELS FOR PLASMAS AND SEMICONDUCTORS

51. IntroductionIn mathematica1 modeling and numerical simulation for plasmas and semiconductorsdevices, the hydrodynamic model like the Euler-Poisson system is wildly used. Due tothe hyperbolic feature of the Euler equations, the study of weak solutions to the Euler-Poisson system is limited in one space dimension. In such situation, the existence of globalweak solutions can be proved under natural assumptions (see [22, 20, 17, 5, 18]). In aseries of papersl1l'l2'l31l4J l we are interested…     

一类各向异性外问题的重叠型区域分解算法

本文以椭圆外调和问题的自然边界归化为基础,提出了求解各向异性常系数椭圆方程的一种重叠型区域分解算法,并分析了算法的收敛性及收敛速度．理论分析及数值实验表明,该方法对于求解各向异性外问题非常有效．     

一类各向异性外问题的非重叠型区域分解算法

In this paper, based on the natural integral operator on elliptic boundary, a nonoverlapping domain decomposition method is presented for a kind of anisotropic elliptic problem with constant coefficients in an exterior domain, and the convergence of the method is analyzed. The choice of the relaxition factor is discussed.Some numerical examples are given. Theoretical analysis as well as numerical examples show that our method is performance.     

JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.     

一类非线性椭圆问题的瀑布型多重网格法

本对二阶非线性椭圆问题提出一种瀑布型多重网格法，数值实验表明该算法非常有效，当d＝1时，给出了理论结果。     

关于并行迭代区域分解算法的松弛因子

1引言考虑二阶椭圆型Dirichlet边值问题的弱形式,求u∈H_0~1(Ω)使得a(u,v)=(f,v),(?) v∈H_0~1(Ω),(1)其中Ω是平面多角形区域,f∈L~2(Ω),(f,v)=∫_Ωfvdx,a(u,v)=∫_Ω(sum from i,j=1 to 2 a_(ij)(?)u/(?)x_i(?)等 a_0uv)dx,其中[a_(ij)]在Ω上对称一致正定,a_(ij)在Ω上分片连续有界,a_0≥0．由Lax-Milgram引理,问题(1)在H_0~1(Ω)中有唯一解．     

一类非对称椭圆问题瀑布型多重网格法

本将瀑布型多重网格法用于求解非对称椭圆边值问题，数值结果表明算法是有效的。     

A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS

1.IntroductionNolloverlappillgdomaindecolllpositionnletllodshavereceivedalotofattentionlenlsilllldallowefficielltparallelisnl.F'Orarecentdevelopmelltofthesemethods,werefertot…     

ON THE CONVERGENCE OF THE NONNESTED V-CYCLE MULTIGRID METHOD FOR NONSYMMETRIC AND INDEFINITE SECOND-ORDER ELLIPTIC PROBLEMS

This paper provides a proof for the uniform convergence rate （independently of the number of mesh levels） for the nonnested V-cycle multigrid method for nonsymmetric and indefinite second-order elliptic problems.