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RECONSTRUCTION OF SCATTERED FIELD FROM FAR-FIELD BY REGULARIZATION

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Journal of Computational Mathematics 2004年第3期22卷 389-402页

作者： Ji-junLiu JinCheng G.Nakamura departmentofmathematics SoutheastUniversityNanjing210096China departmentofmathematics FudanUniversityShanghai200433China departmentofmathematics HokkaidoUniversitySapporo060-0810Japan

In this paper, we consider an inverse scattering problem for an obstacle D R^2 with Robin boundary condition. By applying the point source, we give a regularizing method to recover the scattered field from the far-fie... 详细信息

关键词： Inverse scattering Point source Regularization Numerics

A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E_2 CLASS ELLIPTIC SYSTEMS IN GENERAL FORM

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Applied Mathematics and Mechanics(English Edition) 2003年第2期24卷 163-181页

作者：李明忠徐定华 departmentofmathematics

A class of nonlinear boundary value problems(BVP) for the second_order E 2 class elliptic systems in general form is discussed. By introducing a kind of transformation,this kind of BVP is reduced to a class of generalized nonlinear Riemann_Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.

关键词： elliptic systems boundary value problems singular integral equations singular integral operators existence

MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM

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Journal of Computational Mathematics 2004年第3期22卷 475-488页

作者： Chun-jiaBi Li-kangLi departmentofmathematics YantaiUniversityYantai264005China departmentofmathematics FudanUniversityShanghai200433China

In this paper, we construct and analyse a mortar finite volume method for the discretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.

关键词： Mortar finite volume method Adini element Biharmonic problem

CASCADIC MULTIGRID METHOD FOR ISOPARAMETRIC FINITE ELEMENT WITH NUMERICAL INTEGRATION

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Journal of Computational Mathematics 2004年第1期22卷 123-136页

作者： Chun-jiaBi Li-kangLi departmentofmathematics YantaiUniversityYantai264005China departmentofmathematics FudanUniversityShanghai200433China

The purpose of this paper is to study the cascadic multigrid method for the secondorder elliptic problems with curved boundary in two-dimension which are discretized by the isoparametric finite element method with numerical integration. We show that the CCG method is accurate with optimal complexity and traditional multigrid smoother (likesymmetric Gauss-Seidel, SSOR or damped Jacobi iteration) is accurate with suboptimal complexity.

关键词： Cascadic multigrid method Isoparametric element Numerical integration

NON C^0 NONCONFORMING ELEMENTS FOR ELLIPTIC FOURTH ORDER SINGULAR PERTURBATION PROBLEM

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Journal of Computational Mathematics 2005年第2期23卷 185-198页

作者： Shao-chunChen Yong-chengZhao Dong-yangShi departmentofmathematics ZhengzhouUniversityZhengzhou450052China

In this paper we give a convergence theorem for non C^0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and a twelve parameter rectangular element both with double set parameters, are presented. The convergence and numerical results of the two elements are given.

关键词： Singular perturbation problem Nonconforming element Double set parameter method

New Exact Solution of （N＋1）-Dimensional Burgers System

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Communications in Theoretical Physics 2005年第3期43卷 389-390页

作者： SHENShou-Feng ZHANGJun PANZu-Liang departmentofmathematics ZhejiangUniversityofTechnologyHangzhou310014China／／DepartmentofMathematicsZhejiangUniversityHangzhou310027China departmentofmathematics ZhejiangUniversityofTechnologyHangzhou310014China departmentofmathematics ZhejiangUniversityHangzhou310027China

In this letter, using a Backlund transformation and the new variable separation approach, we find a new general solution of the (N+1)-dimensional Burgers system. The form of the universal formula obtained from many(2+... 详细信息

关键词：变量分离路径 Burgers系统孤波非线性物理

ON A PROBLEM OF SUMS OF MIXED POWERS(II)

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Chinese Annals of Mathematics,Series B 1997年第2期18卷 243-248页

作者： LUMINGGAO YUGANG departmentofmathematics ShanghaiUniversity（JiadingCampus）Shanghai201800 departmentofmathematics UniversityofGeorgiaAthensGA30602

ＯＮＡＰＲＯＢＬＥＭＯＦＳＵＭＳＯＦＭＩＸＥＤＰＯＷＥＲＳ（Ｉ）ＬＵＭＩＮＧＧＡＯＹＵＧＡＮＧＡｂｓｔｒａｃｔＬｅｔＲｂ，ｃ（ｎ）ｄｅｎｏｔｅｔｈｅｎｕｍｂｅｒｏｆｒｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆｎａｓｔｈｅ... 详细信息

ＯＮＡＰＲＯＢＬＥＭＯＦＳＵＭＳＯＦＭＩＸＥＤＰＯＷＥＲＳ（Ｉ）ＬＵＭＩＮＧＧＡＯＹＵＧＡＮＧＡｂｓｔｒａｃｔＬｅｔＲｂ，ｃ（ｎ）ｄｅｎｏｔｅｔｈｅｎｕｍｂｅｒｏｆｒｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆｎａｓｔｈｅｓｕｍｏｆｏｎｅｓｑｕａｒｅ，ｆｏ...

关键词：混合幂渐进公式 Warings问题变量

Multi-component SC Lax Integrable Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System with Two Arbitrary Functions

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Communications in Theoretical Physics 2004年第6X期42卷 807-810页

作者： XIATie-Cheng YUFa-Jun CHENDeng-Yuan ZHANGYi departmentofmathematics BohaiUniversityJinzhou121000China//DepartmentofMathematicsShanghaiUniversityShanghai200436China departmentofmathematics BohaiUniversityJinzhou121000China departmentofmathematics ShanghaiUniversityShanghai200436China departmentofmathematics ZhejiangNormalUniverisityJinhua321004China

A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral *** making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.

关键词：圈代数同位光谱多成分SC松弛分层双层积分

NUMERICAL METHODS FOR MAXWELL＇S EQUATIONS IN INHOMOGENEOUS MEDIA WITH MATERIAL INTERFACES

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Journal of Computational Mathematics 2004年第2期22卷 156-167页

作者： WeiCai departmentofmathematics UniversityofNorthCarolinaatCharlotteCharlotteNC28223USA

In this paper, we will present some recent results on developing numerical methods for solving Maxwell's equations in inhomogeneous media with material interfaces. First,we will present a second order upwinding embedded boundary method - a Cartesian grid based finite difference method with special upwinding treatment near the material interfaces. Second, we will present a high order discontinuous spectral element with Dubinar orthogonal polynomials on triangles. Numerical results on electromagnetic scattering and photonic waveguide will be included.

关键词： Embedded Boundary Methods Discontinuous Galerkin Method Electromagnetic scattering photonic waveguides