In this paper, we investigate the mixed spectral method using generalized Laguerre functions for exterior problems of fourth order partial differential equations. A mixed spectral scheme is provided for the stream fun...In this paper, we investigate the mixed spectral method using generalized Laguerre functions for exterior problems of fourth order partial differential equations. A mixed spectral scheme is provided for the stream function form of the Navier-Stokes equations outside a disc. Numerical results demonstrate the spectral accuracy in space.展开更多
There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, w...There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]展开更多
We establish variational formulation and prove the existence and uniqueness of the three dimen- sional axisymmetric Stokes exterior problem in weighted spaces. Error estimates and convergence for P2 - P0 elements with...We establish variational formulation and prove the existence and uniqueness of the three dimen- sional axisymmetric Stokes exterior problem in weighted spaces. Error estimates and convergence for P2 - P0 elements with infinite element methods are also obtained. Numerical experiments are presented to verify the theoretical analysis.展开更多
In this paper,we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle.Some results on the composite Laguerre-Legendre interpolation,which is a set of piecewise mixed...In this paper,we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle.Some results on the composite Laguerre-Legendre interpolation,which is a set of piecewise mixed interpolations coupled with domain decomposition,are established.As examples of applications,the composite pseudospectral schemes are provided for two model problems.The convergence of proposed schemes are proved.Efficient algorithms are implemented.Numerical results demonstrate the spectral accuracy in space of this new approach.展开更多
From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the...From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.展开更多
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress func...After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.展开更多
The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle.Based on this,the equivalent boundary integral equations(EBIE) with direct variables,whic...The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle.Based on this,the equivalent boundary integral equations(EBIE) with direct variables,which are equivalent to the original boundary value problem,were deduced rigorously.The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.展开更多
In this paper we consider a kind of exterior transmission problem in which the refractive index n（x） is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the ...In this paper we consider a kind of exterior transmission problem in which the refractive index n（x） is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.展开更多
The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physi...The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.展开更多
基金supported by the National Natural Science Foundation of China (No.10871131)the Science and Technology Commission of Shanghai Municipality (No.075105118)+1 种基金the Shanghai Leading Academic Discipline Project (No.S30405)the Fund for E-institutes of Shanghai Universities(No.E03004)
文摘In this paper, we investigate the mixed spectral method using generalized Laguerre functions for exterior problems of fourth order partial differential equations. A mixed spectral scheme is provided for the stream function form of the Navier-Stokes equations outside a disc. Numerical results demonstrate the spectral accuracy in space.
基金the China State Major Key Project for Basic Researches and the Science Fund of the Ministry of Education of China.
文摘There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]
文摘We establish variational formulation and prove the existence and uniqueness of the three dimen- sional axisymmetric Stokes exterior problem in weighted spaces. Error estimates and convergence for P2 - P0 elements with infinite element methods are also obtained. Numerical experiments are presented to verify the theoretical analysis.
基金The work of the first author is supported in part by the Doctor Fund of Henan Univer-sity of Science and Technology No.09001263The work of the second author is sup-ported in part by Science and Technology Commission of Shanghai Municipality,Grant No.75105118+1 种基金the Shanghai Leading Academic Discipline Project No.T0401the Fund for E-institutes of Shanghai Universities No.E03004.
文摘In this paper,we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle.Some results on the composite Laguerre-Legendre interpolation,which is a set of piecewise mixed interpolations coupled with domain decomposition,are established.As examples of applications,the composite pseudospectral schemes are provided for two model problems.The convergence of proposed schemes are proved.Efficient algorithms are implemented.Numerical results demonstrate the spectral accuracy in space of this new approach.
文摘From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.
文摘After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.
文摘The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle.Based on this,the equivalent boundary integral equations(EBIE) with direct variables,which are equivalent to the original boundary value problem,were deduced rigorously.The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.
基金supported by National Natural Science Foundation of People’s Republic of China(11571132 and 11171127)Supported in Part by Program for Changjiang Scholars and Innovative Research Team in University No.IRT13066
文摘In this paper we consider a kind of exterior transmission problem in which the refractive index n（x） is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.
文摘The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.
