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Dehao Yu - One of the best experts on this subject based on the ideXlab platform.
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Natural Boundary Element Method and Hypersingular Integrals
2011Co-Authors: Dehao YuAbstract:The Natural Boundary integral equation is hypersingular integral equation. The hypersingular integrals have some quite different properties from regular and weak singular integrals. A very important topic is how to evaluate the hypersingular integrals efficiently, which should be understand in the Hadamard finite-part sense. The standard numerical integration is not effective for hypersingular integrals, and some special numerical integration should be developed. The method using series expansion of the integral kernel was first suggested by Yu. He solved the harmonic and biharmonic Natural Boundary integral equations on circle successfully. Then numerous works have been devoted to this area. The method of subtracting the singularity, the method of regularization, the approximate integration formulas for finite-part integrals, and the indirect method are also developed. References
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A Coupling of Local Discontinuous Galerkin and Natural Boundary Element
2011Co-Authors: Hongying Huang, Dehao YuAbstract:Summary In this paper, we apply the coupling of local discontinuous Galerkin(LDG) and Natural Boundary element (NBE) methods to solve a class of exterior transmission problems in the plane. As a consequence, the main features of LDG and NBEM are maintained and hence the coupled approach benefits from the advantages of both methods. Referring to \cite{Gatica2010}, we employ LDG subspaces whose functions are continuous on the coupling Boundary. The continuity can be implemented either directly. In this way, the normal derivative becomes the only Boundary unknown, and hence the total number of unknown functions is reduced by two. We prove the stability of the new discrete scheme and derive an a priori error estimate in the energy norm. A numerical example conforming the theoretical result is provided.
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Natural Boundary integral method and related numerical methods
Engineering Analysis With Boundary Elements, 2004Co-Authors: Dehao Yu, Longhua ZhaoAbstract:In this paper, the Natural Boundary integral method and some related numerical methods for solving exterior Boundary value problems are discussed. These different numerical methods are compared, and some numerical examples are given. Those methods based on the Natural Boundary reduction are very efficient and have many extraordinary advantages for exterior problems. Numerical results accord with theoretical analysis very well.
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Schwarz alternating method based on Natural Boundary reduction for time-dependent problems on unbounded domains
Communications in Numerical Methods in Engineering, 2004Co-Authors: Qi-kui Du, Dehao YuAbstract:By using the Natural Boundary reduction an overlapping domain decomposition method is designed to solve some exterior two-dimensional time-dependent parabolic problems. The governing equation is first discretized in time, leading to a sequence of Boundary value problems with respect to time step in an unbounded domain. Then artificial boundaries are introduced. For each time level, an overlapping domain decomposition method, which is based on the Natural Boundary reduction, is constructed to solve the exterior elliptic Boundary value problem on a two-dimensional domain. It is shown that the algorithm is equivalent to Schwarz alternating method. The convergence of this algorithm is given. The contraction factor for the exterior circular domain is also discussed. In the end of this paper, some numerical examples are presented, which illustrate the feasibility and the effectiveness of the proposed methods in this paper. Copyright © 2004 John Wiley & Sons, Ltd.
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Dirichlet--Neumann alternating algorithm based on the Natural Boundary reduction for time-dependent problems over an unbounded domain
Applied Numerical Mathematics, 2003Co-Authors: Qi-kui Du, Dehao YuAbstract:In this paper, a new iterative algorithm to solve a time-dependent problem over an unbounded domain is suggested. This method is based on the Natural Boundary reduction and is suitable for solving initial Boundary value problems of time-dependent wave equation over an unbounded domain. Firstly, an circular artificial Boundary is introduced. Then the original unbounded domain is decomposed into a bounded domain and an exterior unbounded domain outside the artificial Boundary. The Natural integral equation obtained by the Natural Boundary reduction is used as a Boundary condition on the artificial Boundary. Secondly, a Dirichlet-Neumann (D-N) alternating iterative algorithm is constructed. The algorithm is equivalent to preconditioned Richardson iteration method. Thirdly, numerical studies are performed by finite element methods, and the results demonstrate the effectiveness of this algorithm. Finally, some remarks are presented.
Lu Fang-fang - One of the best experts on this subject based on the ideXlab platform.
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Natural Boundary of Random Series
Journal of Xiangfan University, 2020Co-Authors: Lu Fang-fangAbstract:Based on an important lemma on Taylor series and the achievement on S-sum ability and a. s. convergence of symmetric random series,this paper makes a conclusion that the Boundary of convergence of general symmetric random analytic Taylor series is a Natural Boundary.
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The Natural Boundary of Random Series
Acta Analysis Functionalis Applicata, 2020Co-Authors: Lu Fang-fangAbstract:On the basic of an important lemma on the S-summability of analytic series, and the S-summability and a.s. convergenec of symmetric random series. More that the Boundary of convergence of general symmetric random analytic series is a Natural Boundary.
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The Natural Boundary of random series
Journal of Hubei University, 2020Co-Authors: Lu Fang-fangAbstract:By use an important lemma on the S-summability of analytic series,and the S-summability and a.s.convergenec of symmetric random series.More that the Boundary of convergence of general symmetric random analytic series is a Natural Boundary.Especially,for symmetric random Taylor series,random Dirichlet series,random Laurent series and so on,the boundaries of convergence of these series are Natural boundaries.
Li Shun-cai - One of the best experts on this subject based on the ideXlab platform.
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The Natural Boundary Element Method for the Bending of the Elastic Thin Circular Plate under the Discontinuous Load
Journal of Guangdong University of Technology, 2020Co-Authors: Li Shun-caiAbstract:Some singularity functions are introuduced to express the generalized distribution surface density of the transverse discontinuous load on the circular plate. Based on the Natural Boundary reduction for the Boundary value problems of biharmonic equation, the bending solutions to the circular plate under the discontinuous load are obtained.
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Natural Boundary element method and its application in the bending problem of the elastic thin circular plate
Journal of Shaanxi Institute of Technology, 2020Co-Authors: Li Shun-caiAbstract:FENG Kang, YU De-hao and some other scholars of our country are the first ones to create the Natural Boundary element method (NBEM), and they have successfully studied the Natural Boundary reduction method for the Boundary value problems of harmonic equation and biharmonic equation. Based on the Natural Boundary reduction for the Boundary value problems of biharmonic equation, the Poisson integral formula on the bending deflection of the thin circular plate and its Natural integral equations of Boundary internal forces are presented. By means of the numerical method of strongly singular integrals, the bending solutions to the thin circular plate are obtained, and the feasibility of this method has been confirmed in practice.
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Darcy-Stokes Equations with Finite Difference and Natural Boundary Element Coupling Method
Cmes-computer Modeling in Engineering & Sciences, 2011Co-Authors: Peng Weihong, Cao Guohua, Dongzhengzhu, Li Shun-caiAbstract:Numerical method is applied to investigate the Darcy-Stokes equations, which is governing the steady incompressible Stokes flow past a circular cavity in a porous medium. The free fluid flow is modeled by the incompressible Stokes equations, and the flow in the porous medium is imposed by Darcy equations. Based on domain decomposition method with D-N alternating iteration algorithm, the coupling method of finite difference method and Natural Boundary element method is studied for the coupling Darcy-Stokes equations under a certain pressure difference. Divide the whole domain into two non-intersecting bounded subdomains and . The Boundary of cavity is the artificial Boundary . The fan shaped grid is used to mesh in polar coordinates. Then, the finite difference method is applied to resolve the Darcy’ law in domain . Thus, the pressure at arbitrary node can be attained. According to the relationship of velocity and pressure, the radial velocity and tangential velocity on the artificial Boundary would be acquired. Afterwards, based on Newton-Cotes numerical integration formula, utilize the velocity value on artificial Boundary and calculate in domain with Natural Boundary element method. Remarkably, the initial pressure value should be given before iterating, and the new value on the artificial Boundary can be obtained with finite difference method in domain . Finally, the Natural Boundary element method is applied in domain and the new pressure value will be educed again. Iterate in turn, the results will be achieved with rational precision. As to the steady-state parallel flow with a void space, the velocity is increasing with the permeability coefficient under the same pressure difference. The horizontal velocity is rapidly decreasing with the raise of the distance from the center, and increasing slowly to the undisturbed velocity in order to fill the continuity condition on the artificial Boundary. The velocity vector distribution can also be obtained by the finite difference and Natural Boundary element coupling method. The numerical results indicate that the finite difference and Natural Boundary element coupling method is efficient and convenient for the Darcy-Stokes problem of the steady-state parallel flow with a void space.
Qi-kui Du - One of the best experts on this subject based on the ideXlab platform.
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Schwarz alternating method based on Natural Boundary reduction for time-dependent problems on unbounded domains
Communications in Numerical Methods in Engineering, 2004Co-Authors: Qi-kui Du, Dehao YuAbstract:By using the Natural Boundary reduction an overlapping domain decomposition method is designed to solve some exterior two-dimensional time-dependent parabolic problems. The governing equation is first discretized in time, leading to a sequence of Boundary value problems with respect to time step in an unbounded domain. Then artificial boundaries are introduced. For each time level, an overlapping domain decomposition method, which is based on the Natural Boundary reduction, is constructed to solve the exterior elliptic Boundary value problem on a two-dimensional domain. It is shown that the algorithm is equivalent to Schwarz alternating method. The convergence of this algorithm is given. The contraction factor for the exterior circular domain is also discussed. In the end of this paper, some numerical examples are presented, which illustrate the feasibility and the effectiveness of the proposed methods in this paper. Copyright © 2004 John Wiley & Sons, Ltd.
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Dirichlet--Neumann alternating algorithm based on the Natural Boundary reduction for time-dependent problems over an unbounded domain
Applied Numerical Mathematics, 2003Co-Authors: Qi-kui Du, Dehao YuAbstract:In this paper, a new iterative algorithm to solve a time-dependent problem over an unbounded domain is suggested. This method is based on the Natural Boundary reduction and is suitable for solving initial Boundary value problems of time-dependent wave equation over an unbounded domain. Firstly, an circular artificial Boundary is introduced. Then the original unbounded domain is decomposed into a bounded domain and an exterior unbounded domain outside the artificial Boundary. The Natural integral equation obtained by the Natural Boundary reduction is used as a Boundary condition on the artificial Boundary. Secondly, a Dirichlet-Neumann (D-N) alternating iterative algorithm is constructed. The algorithm is equivalent to preconditioned Richardson iteration method. Thirdly, numerical studies are performed by finite element methods, and the results demonstrate the effectiveness of this algorithm. Finally, some remarks are presented.
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Natural Boundary Element Method for Elliptic Boundary Value Problems in Domains with Concave Angle
Journal of Marine Science and Technology, 2001Co-Authors: Qi-kui Du, Dehao YuAbstract:In this paper the Natural Boundary reduction for some elliptic Boundary value problems with concave angle domains and its Natural Boundary element methods are investigated. Natural integral equations and Poisson integral formulae are given. A finite element methods of Natural integral equations are discussed in details. The convergence of approximate solutions and their error estimates are obtained. Some numerical experiments are presented to demonstrate the performance of the method and our estimates. As an application, we present the coupling of FEM and Natural Boundary element.
Ming-chang Wu - One of the best experts on this subject based on the ideXlab platform.
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Effect of Natural Boundary condition and the neutral surface of nonlinear type on the upper-bound solution to upset forging of rings using a variational approach
Mechanics of Materials, 2008Co-Authors: Ming-chang WuAbstract:Abstract The purpose of this work is to investigate the effect of Natural Boundary condition and the type of neutral surface on the upper-bound solutions using a variational approach. To this end, the neutral surface of the upset ring was considered a function of polynomials of various orders during deformation process, and then an upper-bound forming energy equation was formulated in terms of the function as well as the velocity field derived from the theory of stream function. Since the velocity field had been expressed in terms of an implicit stream function before the upper-bound forming energy equation J was established, a variational approach was fulfilled to determine an upper-bound solution by extremizing J. As a result, a set of Boundary conditions was derived mathematically. To determine the upper-bound solution, the derived Boundary conditions, which include the so-called Natural Boundary conditions and kinematically Boundary conditions, were imposed in an optimization procedure. Such a method we have proposed to determine the solution is particularly termed the variational upper-bound (VUB) method in order to distinguish it from the traditional upper-bound (UB) method, which usually ignores the Natural Boundary condition perceptibly unobtainable. The Natural Boundary condition can be physically interpreted as to constrain plastic flow of the upset ring at frictional interfaces. However, in order to investigate the effect of the type of neutral surface on upper-bound solutions, a polynomial that may result in the neutral surface of nonlinear type was proposed. By comparing with some experimental results, it is found that the VUB method has considerably improved on the UB method in predicting the calibration curves, the bulged profiles of upset ring and disks, and the forming energy. The result presented in this work also demonstrates that the effect of the Natural Boundary condition is much more pronounced than that of the type of neutral surface used on improving the upper-bound solution. While keeping the same number of free parameters left for the purpose of minimization procedure, the VUB method is permitted to establish an approximate solution of higher order than the UB method, because it additionally satisfies the Natural Boundary condition derived in this work. The finite element solution determined using MARC, a commercial software package, is also presented in this work for discussion.
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Effect of Natural Boundary conditions on the upper-bound analysis of upset forging of ring and disks
Materials & Design, 2006Co-Authors: Ming-chang WuAbstract:The purpose of this investigation is to discuss the effect of Natural Boundary conditions derived using the method of variational calculus for upset forging of rings. In order to derive the Natural Boundary condition, an assumed admissible function with unknown constants is replaced by an arbitrary function. Rather than minimizing the unknown constants in the assumed function, the arbitrary function is found using variational calculus, and the Natural Boundary condition is derived as a consequence. The upper-bound solutions, with and without imposing the Natural Boundary condition, as well as finite element solutions were compared and discussed. The finite element solutions were determined using the commercial software package MARC. All solutions were experimentally verified using the experimental result of the calibration curve from ring tests. They were then discussed, by comparing with experimental bulged profiles as well as experimental forming load. From the result, we can clearly indicate that the Natural Boundary condition, which constrains plastic flow of the upsetting ring on the contact interface, significantly affects the upper-bound solution not only in predicting the bulge profile of the upset ring, but also in calculating the total forming load. The variational upper-bound solution, which accounts for the Natural Boundary condition, has shown to present a significant improvement on the traditional upper-bound solution in general.
