The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundar...The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.展开更多
The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boun...The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.展开更多
The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived ...The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.展开更多
In earlier approach, the 2-D acoustical field profiles on the substrate region are often calculated with BPM. In this paper, we present a new approach based on the finite element -artificial transmitting boundary meth...In earlier approach, the 2-D acoustical field profiles on the substrate region are often calculated with BPM. In this paper, we present a new approach based on the finite element -artificial transmitting boundary method and calculate acoustical field on the substrate region.展开更多
This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neuman...This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded domain.For the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory storage.High order fully discrete schemes,both second-order in time and space,are given to discretize two reduced problems.Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.展开更多
This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary c...This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)problem.After that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability analysis.The delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically investigated.Finally,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.展开更多
In this paper we use an analytical-numerical approach to find,in a systematic way,new 1-soliton solutions for a discrete sine-Gordon system in one spatial dimension.Since the spatial domain is unbounded,the numerical ...In this paper we use an analytical-numerical approach to find,in a systematic way,new 1-soliton solutions for a discrete sine-Gordon system in one spatial dimension.Since the spatial domain is unbounded,the numerical scheme employed to generate these soliton solutions is based on the artificial boundary method.A large selection of numerical examples provides much insight into the possible shapes of these new 1-solitons.展开更多
基金supported by National National Science Foundation of China(Grant No.10971116)FRG of Hong Kong Baptist University(Grant No.FRG1/11-12/051)
文摘The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.
文摘The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.
基金subsidized by the National Basic Research Program of China under the grant 2005CB321701the National Natural Science Foundation of China under the grant 10531080the Beijing Natural Science Foundation under the grant 1072009 and the Research Project of Zhejiang Ocean University (X08M013,X08Z04)
文摘The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
基金This work was supported by the National Natural Science Fund of China (10084001) the Action Plan for Booming Education of Tianjin University.
文摘In earlier approach, the 2-D acoustical field profiles on the substrate region are often calculated with BPM. In this paper, we present a new approach based on the finite element -artificial transmitting boundary method and calculate acoustical field on the substrate region.
基金This research is supported in part by the U.S.NSF grants DMS-1318586 and DMS-1315259AFOSR MURI Center for Material Failure Prediction Through Peridynamics,OSD/ARO/MURI W911NF-15-1-0562 on Fractional PDEs for Conservation Laws and Beyond:Theory,Numerics and Applicationsthe NSFC under grants 91430216 and the NSFC program for Scientific Research Center under program No.:U1530401.
文摘This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded domain.For the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory storage.High order fully discrete schemes,both second-order in time and space,are given to discretize two reduced problems.Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.
基金This work is supported in part by the National Natural Science Foun-dation of China(Grant Nos.11771162,11771035,11571027,91430216 and U1530401)Beijing Nova Program(No.Z151100003150140)Scientific Research Project of Beijing Educational Committee(No.KM201510005032).
文摘This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)problem.After that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability analysis.The delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically investigated.Finally,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.
基金The research was supported in part by the Natural Sciences and Engineering Research Council(NSERC)of Canada,by Hong Kong Research Grants Council and FRG of Hong Kong Baptist University.
文摘In this paper we use an analytical-numerical approach to find,in a systematic way,new 1-soliton solutions for a discrete sine-Gordon system in one spatial dimension.Since the spatial domain is unbounded,the numerical scheme employed to generate these soliton solutions is based on the artificial boundary method.A large selection of numerical examples provides much insight into the possible shapes of these new 1-solitons.
