This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, th...This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.展开更多
With the development of distribution automation system, the centralized meter reading system has been adopted more and more extensively, which provides real-time electricity consumption data of end-users, and conseque...With the development of distribution automation system, the centralized meter reading system has been adopted more and more extensively, which provides real-time electricity consumption data of end-users, and consequently lays foundation for operating condition on-line analysis of distribution network. In this paper, a modified back/forward sweep method, which directly uses real-time electricity consumption data acquired from the centralized meter reading system, is proposedto realize voltage analysis based on 24-hour electricity consumption data of a typical transformer district. Furthermore, the calculated line losses are verified through data collected from the energy metering of the distribution transformer, illustrating that the proposed method can be applied in analyzing voltage level and discovering unknown energy losses, which will lay foundation for on-line analysis, calculation and monitoring of power distribution network.展开更多
A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-or...A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.展开更多
A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some...A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calcu...A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calculated when the ESs operate at their maximum reactive power either in the inductive or capacitive modes.The power rating of the ES is adjusted on the basis of the available active power at the bus.And in the optimization problem,it is expressed as the power ratio of the noncritical load(NCL)and critical load(CL).The implemented ES model is flexible,which can be used on any bus and any phase.The model determines the output voltage from the parameters and operating conditions at the point of common coupling(PCC).These conditions are integrated using the backward/forward sweep method(BFSM)and are updated during power flow calculations.The problem is described as a mixed-integer nonlinear problem and solved efficiently using an improved BFSM-based genetic algorithm,which computes power flow and ES placement simultaneously.The effectiveness of this method is evaluated through testing in IEEE 13-bus and 34-bus systems.展开更多
The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel ...The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel method. The variations of aerodynamic characteristics of Canard-FSW configurations with different positions of the canard are investigated,finding that the aerodynamic interference and mutual coupling effect between the canard and main wing have made great contributions to the lift and stability characteristics of the whole aircraft. Canard can radically improve the surface flow pattern of the main wing. And its own vortex can have a favorable interference on the main wing and can effectively control the airflow boundary layer separation. At small angles of attack,the aerodynamic characteristics are sensitive to the positions of the canard and the main wing,but at high angles of attack,the aerodynamic performances of the configuration are not only related to the shape of the canard （forward or backward）,but also with the size of control force as well as the features of the vortices generated above the main wing and the canard. The different configurations and vortices are illustrated using the velocity vector,streamlines and pressure contours.展开更多
In this paper,we propose a new numerical method which is a least squares approximaton based on pseudospectral method for the Forward-Backward heat equation. The existence and uniqueness of the solution of the least sq...In this paper,we propose a new numerical method which is a least squares approximaton based on pseudospectral method for the Forward-Backward heat equation. The existence and uniqueness of the solution of the least squares approximation are proved. Error estimates for this approximation are given,which show that tile order of convergence depends only on the regularity of tile solution and the right hand of the Forward-Backward heat equation.展开更多
In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. T...In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.展开更多
By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic d...By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.展开更多
The forward-backward heat equation arises in a remarkable variety of physical applications. A non-overlaping domain decomposition method was constructed to obtain numerical solutions of the forward-backward heat equa...The forward-backward heat equation arises in a remarkable variety of physical applications. A non-overlaping domain decomposition method was constructed to obtain numerical solutions of the forward-backward heat equation. The primary advantage is that the method reduces the computation time tremendously. The convergence of the given method is established. The numerical performance shows that the domain decomposition method is effective.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 60571058)the National Defense Foundation of China
文摘This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.
文摘With the development of distribution automation system, the centralized meter reading system has been adopted more and more extensively, which provides real-time electricity consumption data of end-users, and consequently lays foundation for operating condition on-line analysis of distribution network. In this paper, a modified back/forward sweep method, which directly uses real-time electricity consumption data acquired from the centralized meter reading system, is proposedto realize voltage analysis based on 24-hour electricity consumption data of a typical transformer district. Furthermore, the calculated line losses are verified through data collected from the energy metering of the distribution transformer, illustrating that the proposed method can be applied in analyzing voltage level and discovering unknown energy losses, which will lay foundation for on-line analysis, calculation and monitoring of power distribution network.
基金Supported by National Science Foundation of China(Grant 10871179)the National Basic Research Programme of China(Grant 2008CB717806)the Department of Education of Zhejiang Province(GrantY200803559).
文摘A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.
基金supported by the National Natural Science Foundation of China (No. 10771122)the NaturalScience Foundation of Shandong Province of China (No. Y2006A08)the National Basic ResearchProgram of China (973 Program) (No. 2007CB814900)
文摘A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
基金supported by Consejo Nacional de Humanidades,Ciencia y Tecnología(CONAHCYT)—México(No.863547)the fellowship 2021-000001-01NACF-00604 given to the G.H.Valencia-Riverathe scholarships 175599,64698,253652,and 296574,given to G.Tapia-Tinoco,A.Garcia-Perez,D.Granados-Lieberman,and M.Valtierra-Rodriguez,respectively,through the Sistema Nacional de Investigadoras e Investigadores(SNII)-CONAHCYT-México.
文摘A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calculated when the ESs operate at their maximum reactive power either in the inductive or capacitive modes.The power rating of the ES is adjusted on the basis of the available active power at the bus.And in the optimization problem,it is expressed as the power ratio of the noncritical load(NCL)and critical load(CL).The implemented ES model is flexible,which can be used on any bus and any phase.The model determines the output voltage from the parameters and operating conditions at the point of common coupling(PCC).These conditions are integrated using the backward/forward sweep method(BFSM)and are updated during power flow calculations.The problem is described as a mixed-integer nonlinear problem and solved efficiently using an improved BFSM-based genetic algorithm,which computes power flow and ES placement simultaneously.The effectiveness of this method is evaluated through testing in IEEE 13-bus and 34-bus systems.
基金National Defense Basic Research Program (B222006060)
文摘The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel method. The variations of aerodynamic characteristics of Canard-FSW configurations with different positions of the canard are investigated,finding that the aerodynamic interference and mutual coupling effect between the canard and main wing have made great contributions to the lift and stability characteristics of the whole aircraft. Canard can radically improve the surface flow pattern of the main wing. And its own vortex can have a favorable interference on the main wing and can effectively control the airflow boundary layer separation. At small angles of attack,the aerodynamic characteristics are sensitive to the positions of the canard and the main wing,but at high angles of attack,the aerodynamic performances of the configuration are not only related to the shape of the canard （forward or backward）,but also with the size of control force as well as the features of the vortices generated above the main wing and the canard. The different configurations and vortices are illustrated using the velocity vector,streamlines and pressure contours.
文摘In this paper,we propose a new numerical method which is a least squares approximaton based on pseudospectral method for the Forward-Backward heat equation. The existence and uniqueness of the solution of the least squares approximation are proved. Error estimates for this approximation are given,which show that tile order of convergence depends only on the regularity of tile solution and the right hand of the Forward-Backward heat equation.
基金The project was supported by National Science Foundation （Grant No. 10471129）.
文摘In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.
基金supported by the NSF of China(No.12001539)the NSF of Hunan Province(No.2020JJ5647)China Postdoctoral Science Foundation(No.2019TQ0073).
文摘By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.
基金Supported by the Special Funds for Major State BasicResearch Projects of China (No.G19990 32 80 2 )
文摘The forward-backward heat equation arises in a remarkable variety of physical applications. A non-overlaping domain decomposition method was constructed to obtain numerical solutions of the forward-backward heat equation. The primary advantage is that the method reduces the computation time tremendously. The convergence of the given method is established. The numerical performance shows that the domain decomposition method is effective.
