作者：
Qiya HuLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100080 China.
A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and *** is shown that the new normal-like derivatives,which are called the generalized normal derivative...
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A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and *** is shown that the new normal-like derivatives,which are called the generalized normal derivatives,preserve the major prop- erties of the existing standard normal *** generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order el- liptic *** approximate solutions generated by these methods still possess the optimal energy-norm error estimates,even if the exact solutions to the underlying elliptic problems admit very low regularities.
Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution...
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Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.
In this paper we are concerned with the construction of a preconditioner for the Steklov-Poincaré operator arising from a non-overlapping domain decomposition method for second-order elliptic problems in three-di...
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ISBN:
(纸本)9783540751984
In this paper we are concerned with the construction of a preconditioner for the Steklov-Poincaré operator arising from a non-overlapping domain decomposition method for second-order elliptic problems in three-dimensional domains. We first propose a new kind of multilevel decomposition of the finite element space on the interface associated with a general quasi-uniform triangulation. Then, we construct a multilevel preconditioner for the underlying Steklov-Poincaré operator. The new multilevel preconditioner enjoys optimal computational complexity, and almost optimal convergence rate.
作者：
DU QiangMING PingBingDepartment of Mathematics
Pennsylvania State UniversityUniversity ParkPA 16802USA LSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijing 100190China
In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some c...
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In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the *** new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular *** error bound sare derived for both smooth and non-smooth *** strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
作者：
Dier ZhangAihui ZhouXin-Gao GongDepartment of Physics
Fudan UniversityShanghai 200433China LSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China
The finite element method is a promising method for electronic structure *** this paper,a new parallelmesh refinementmethod for electronic structure calculations is *** properties of the method are investigated to mak...
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The finite element method is a promising method for electronic structure *** this paper,a new parallelmesh refinementmethod for electronic structure calculations is *** properties of the method are investigated to make itmore efficient andmore convenient for *** practical issues such as distributed memory parallel computation,less tetrahedra prototypes,and the assignment of the mesh elements carried out independently in each sub-domain will be *** numerical experiments on the periodic system,cluster and nano-tube are presented to demonstrate the effectiveness of the proposed method.
Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and *** relationships between the finite element method and the finite differe...
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Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and *** relationships between the finite element method and the finite difference method are addressed,too.
Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rat...
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Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.
We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the k...
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We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.
A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hi...
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A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.
In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′...
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In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′elec element equations,*** combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform *** also present some numerical experiments to demonstrate the theoretical results.
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