In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a...In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a good application prospect.Firstly,a numerical virtual flight simulation model based on overlapping dynamic mesh technology is constructed.In order to verify the accuracy of the dynamic grid technology and the calculation of unsteady flow,a numerical simulation of the basic finner projectile without control is carried out.The simulation results are in good agreement with the experiment data which shows that the algorithm used in this paper can also be used in the design and evaluation of the intelligent controller in the numerical virtual flight simulation.Secondly,combined with the real-time control requirements of aerodynamic,attitude and displacement parameters of the projectile during the flight process,the numerical simulations of the basic finner projectile’s pitch channel are carried out under the traditional PID(Proportional-Integral-Derivative)control strategy and the intelligent PID control strategy respectively.The intelligent PID controller based on BP(Back Propagation)neural network can realize online learning and self-optimization of control parameters according to the acquired real-time flight parameters.Compared with the traditional PID controller,the concerned control variable overshoot,rise time,transition time and steady state error and other performance indicators have been greatly improved,and the higher the learning efficiency or the inertia coefficient,the faster the system,the larger the overshoot,and the smaller the stability error.The intelligent control method applying on numerical virtual flight is capable of solving the complicated unsteady motion and flow with the intelligent PID control strategy and has a strong promotion to engineering application.展开更多
The frequent change in ice drift direction poses a significant challenge for turret moored ship in ice. Variability in ice drift is mainly caused by the winds and currents. To solve this problem, a new method with num...The frequent change in ice drift direction poses a significant challenge for turret moored ship in ice. Variability in ice drift is mainly caused by the winds and currents. To solve this problem, a new method with numerical simulation based on heading control is applied to reduce the risk of operation of The Arctic Tandem Offloading Terminal(ATOT),which includes an offloading icebreaker(OIB) moored to a submerged turret and a shuttle tanker moored at the stern of the OIB in this paper. An icebreaking tanker, MT Uikku, was modeled in a simulation program. Then the level ice load on the tanker was calculated with different ice thicknesses and drift speeds, after which a heading controller assisted with mooring system is used to simulate the horizontal motion of the tanker under the ice action.展开更多
A new method for suppressing cutting chatter is studied by adjusting servo parameters of the numerical control （NC） machine tool and controlling the limited cutting width. A model of the cutting system of the NC mac...A new method for suppressing cutting chatter is studied by adjusting servo parameters of the numerical control （NC） machine tool and controlling the limited cutting width. A model of the cutting system of the NC machine tool is established. It includes the mechanical system, the servo system and the cutting chatter system. Interactions between every two systems are shown in the model. The cutting system stability is simulated and relation curves between the limited cutting width and servo system parameters are described in the experiment. Simulation and experimental results show that there is a mapping relation between the limited cutting width and servo parameters of the NC machine tool, and the method is applicable and credible to suppress chatter.展开更多
Mine or longwall panel layout is a 3D structure with highly non-uniform stress distribution. Recognition of such fact will facilitate underground problem identification/investigation and solving by numerical modeling ...Mine or longwall panel layout is a 3D structure with highly non-uniform stress distribution. Recognition of such fact will facilitate underground problem identification/investigation and solving by numerical modeling through proper model construction. Due to its versatility, numerical modeling is the most popular method for ground control design and problem solving. However numerical modeling results require highly experienced professionals to interpret its validity/applicability to actual mining operations due to complicated mining and geological conditions. Underground ground control monitoring is routinely performed to predict roof behavior such as weighting and weighting interval without matching observation of face mining condition while the mining pressures are being monitored, resulting in unrealistic interpretation of the obtained data on mining pressure. The importance of ground control pressure monitoring and simultaneous observation of mining and geological conditions is illustrated by an example of shield leg pressure monitoring and interpretation in an U.S. longwall coal mine: it was found that the roof strata act like a plate, not an individual block of the size of a shield dimension, as commonly assumed by all researchers and shield capacity is not a fixed property for a longwall panel or a mine or a coal seam. A new mechanism on the interaction between shield's hydraulic leg pressure and roof strata for shield loading is proposed.展开更多
In order to study the strength-weakening law of roofs of water-rich roadway, this study used FLAC software, and simulated and analyzed the failure characteristics of the surrounding rock of water-rich roadway under th...In order to study the strength-weakening law of roofs of water-rich roadway, this study used FLAC software, and simulated and analyzed the failure characteristics of the surrounding rock of water-rich roadway under the condition of different cross sections and support parameters, finally obtained the stress distribution of the principle stress of the roadway as well as the displacement variation of its surrounding rock. Results indicate that the roof stability of roadway with semicircular cross section is better than the roadway with inclined rectangular cross section under water-rich condition. Besides, the surrounding rock deformation of roadway under the action of water shows a pronounced increase compared to the roadway without the action of water due to the fact that water will obviously weaken the surrounding rock of roadway, especially its roof. It is very beneficial to control roof stability of water-rich roadway and guarantee the roadway stability during its service life by improving the pretension of bolt and cable as well as decreasing inter-row spacing of the bolt.展开更多
A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a diel...A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a dielectric barrier discharge actuator is modeled with a phenomenological method for plasma simulation coupled with the compressible Navier-Stokes equations. The governing equations are solved using an efficient implicit finitevolume method. The responses of the separated flow field to the effects of an unsteady body force in various inter- pulses and duty cycles as well as different locations and magnitudes are studied. It is shown that the duty cycle and inter-pulse are key parameters for flow separation control. Additionally, it is concluded that the body force is able to attach the flow and can affect boundary layer grow that Mach number 0.1 and Reynolds number of 45000.展开更多
A novel distributed numerical control (DNC) integrated system based on plug-in software technology is proposed. It connects new or old numerical control (NC) machine tools which have inhomogeneous numerical control sy...A novel distributed numerical control (DNC) integrated system based on plug-in software technology is proposed. It connects new or old numerical control (NC) machine tools which have inhomogeneous numerical control systems with CAD/CAM system by CANbus network. A DNC computer is able to control 15 sets of NC machine tools reliably at the same time. The novel DNC system increases the efficiency of machine tools and improve the production management level by realizing non-paper production, agile manufacturing, networked manufacturing and so on in the near future. Key technologies to construct the novel DNC integrated system include the integration of inhomogeneous numerical control systems, NC program restart, and algorithm for communication competition. Such system has demonstrated successful applications in some corporations that have acquired good economic benefits and social effects.展开更多
Based on the Fourier–Chebyshev spectral method, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with direct numerical simulation(DNS...Based on the Fourier–Chebyshev spectral method, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with direct numerical simulation(DNS) methods for different Reynolds numbers. A formula is derived to express the relation between fluctuating velocities and the friction drag coefficient. With the application of electromagnetic force, the in-depth relations among the fluctuating velocities near the wall, Reynolds stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The fluctuating velocities along the streamwise and normal directions are suppressed significantly,while the fluctuating velocity along the spanwise direction is enhanced dramatically due to the spanwise electromagnetic force. However, the values of Reynolds stress depend on the fluctuating velocities along the streamwise and normal directions rather than that along the spanwise direction. Therefore, the significant effect of drag reduction is obtained. Moreover,the maximum drag reduction is weakened due to the decay of control effect for fluctuating velocities as the Reynolds number increases.展开更多
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
This paper investigates the synchronization of a fractional order hyperchaotic system using passive control. A passive controller is designed, based on the properties of a passive system. Then the synchronization betw...This paper investigates the synchronization of a fractional order hyperchaotic system using passive control. A passive controller is designed, based on the properties of a passive system. Then the synchronization between two fractional order hyperchaotic systems under different initial conditions is realized, on the basis of the stability theorem for fractional order systems. Numerical simulations and circuitry simulations are presented to verify the analytical results.展开更多
To obtain the performance characteristics of hydrodynamic tractor-retarder assembly under traction work condition,a numerical simulation model of flow channel was established and tetrahedron unstructured grids were ad...To obtain the performance characteristics of hydrodynamic tractor-retarder assembly under traction work condition,a numerical simulation model of flow channel was established and tetrahedron unstructured grids were adopted in the meshing stage.The racing rotating speed of the brake wheels was calculated by computational fluid dynamics（CFD） calculation and interpolation,and then accurate boundary condition was applied to the CFD simulation to study the pressure and velocity distribution of internal flow field in hydrodynamic tractor-retarder assembly.Finally,the original characteristics were calculated by CFD post-processing analysis.Comparison of experimental data and flow field analysis results showed that the calculation tolerance of the torque ratio K and the efficiency η was less than 5%,and the calculation tolerance of the pump torque coefficient λ was less than 10%.展开更多
In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104〈Re〈1.54&#...In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104〈Re〈1.54×106. The calculations were performed by means of solving the 2-D Unsteady Reynolds-Averaged Navier-Stokes （URANS） equations with a k-ε turbulence model. The calculated results, produced flow structure drag and lift coefficients, as well as Strouhal numbers. The findings were in good agreement with previous published data, which also supplied us with a good understanding of the flow across cylinders of different high Reynolds numbers. Meanwhile, an effective measure was presented to control the lift force on a cylinder, which points the way to decrease the vortex induced vibration of marine structure in future.展开更多
Gelled particles can be transferred deeply inside oil reservoirs to block water channels due to their physicochemical characteristics, including swelling, deformation, and synergetic effect （reacting with polymers）,...Gelled particles can be transferred deeply inside oil reservoirs to block water channels due to their physicochemical characteristics, including swelling, deformation, and synergetic effect （reacting with polymers）, and then the injection profiles are significantly modified. At present, research on gelled particles is mainly focused on laboratory studies of drive mechanisms, and rarely on mathematical models describing the blocking process of gelled particles. In this paper, the blocking process of gelled particles is divided into two sub-processes： deposition and desorption due to particle deformation. A mathematical model based on filtration theory is proposed considering the effect of characteristics of gelled particles on the blocking process. Blocking laws were simulated and researched using the mathematical model. Results of the simulation of the blocking of gelled particles are quite consistent with the experimental results, which confirms the reliability of the mathematical model developed.展开更多
The primary issue regarding the plasma synthetic jet actuator(PSJA)is its performance attenuation at high frequencies.To solve this issue,a self-supplementing,dual-cavity,plasma synthetic jet actuator(SD-PSJA)is desig...The primary issue regarding the plasma synthetic jet actuator(PSJA)is its performance attenuation at high frequencies.To solve this issue,a self-supplementing,dual-cavity,plasma synthetic jet actuator(SD-PSJA)is designed,and the static properties of the SD-PSJA are investigated through experiments and numerical simulations.The pressure measurement shows that the SD-PSJA has two saturation frequencies(1200 Hz and 2100 Hz),and the experimental results show that both the saturation frequencies decrease as the volume of the bottom cavity of the SD-PSJA increases.As the size of the supplement hole increases,the first saturation frequency increases continuously,while the second saturation frequency shows a trend of first decreasing and then increasing.Numerical simulations show that the working process of the SD-PSJA is similar to that of the PSJA,but the volume of the cavity in the SD-PSJA is smaller than that of the PSJA;the SD-PSJA can supplement air to the top cavity through two holes,thus reducing the refresh time and effectively improving the jet intensity of the actuator at high frequencies.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
文摘In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a good application prospect.Firstly,a numerical virtual flight simulation model based on overlapping dynamic mesh technology is constructed.In order to verify the accuracy of the dynamic grid technology and the calculation of unsteady flow,a numerical simulation of the basic finner projectile without control is carried out.The simulation results are in good agreement with the experiment data which shows that the algorithm used in this paper can also be used in the design and evaluation of the intelligent controller in the numerical virtual flight simulation.Secondly,combined with the real-time control requirements of aerodynamic,attitude and displacement parameters of the projectile during the flight process,the numerical simulations of the basic finner projectile’s pitch channel are carried out under the traditional PID(Proportional-Integral-Derivative)control strategy and the intelligent PID control strategy respectively.The intelligent PID controller based on BP(Back Propagation)neural network can realize online learning and self-optimization of control parameters according to the acquired real-time flight parameters.Compared with the traditional PID controller,the concerned control variable overshoot,rise time,transition time and steady state error and other performance indicators have been greatly improved,and the higher the learning efficiency or the inertia coefficient,the faster the system,the larger the overshoot,and the smaller the stability error.The intelligent control method applying on numerical virtual flight is capable of solving the complicated unsteady motion and flow with the intelligent PID control strategy and has a strong promotion to engineering application.
文摘The frequent change in ice drift direction poses a significant challenge for turret moored ship in ice. Variability in ice drift is mainly caused by the winds and currents. To solve this problem, a new method with numerical simulation based on heading control is applied to reduce the risk of operation of The Arctic Tandem Offloading Terminal(ATOT),which includes an offloading icebreaker(OIB) moored to a submerged turret and a shuttle tanker moored at the stern of the OIB in this paper. An icebreaking tanker, MT Uikku, was modeled in a simulation program. Then the level ice load on the tanker was calculated with different ice thicknesses and drift speeds, after which a heading controller assisted with mooring system is used to simulate the horizontal motion of the tanker under the ice action.
文摘A new method for suppressing cutting chatter is studied by adjusting servo parameters of the numerical control （NC） machine tool and controlling the limited cutting width. A model of the cutting system of the NC machine tool is established. It includes the mechanical system, the servo system and the cutting chatter system. Interactions between every two systems are shown in the model. The cutting system stability is simulated and relation curves between the limited cutting width and servo system parameters are described in the experiment. Simulation and experimental results show that there is a mapping relation between the limited cutting width and servo parameters of the NC machine tool, and the method is applicable and credible to suppress chatter.
基金supported by the National Natural Science Foundation of China (Nos. 51604267 and 51704095)
文摘Mine or longwall panel layout is a 3D structure with highly non-uniform stress distribution. Recognition of such fact will facilitate underground problem identification/investigation and solving by numerical modeling through proper model construction. Due to its versatility, numerical modeling is the most popular method for ground control design and problem solving. However numerical modeling results require highly experienced professionals to interpret its validity/applicability to actual mining operations due to complicated mining and geological conditions. Underground ground control monitoring is routinely performed to predict roof behavior such as weighting and weighting interval without matching observation of face mining condition while the mining pressures are being monitored, resulting in unrealistic interpretation of the obtained data on mining pressure. The importance of ground control pressure monitoring and simultaneous observation of mining and geological conditions is illustrated by an example of shield leg pressure monitoring and interpretation in an U.S. longwall coal mine: it was found that the roof strata act like a plate, not an individual block of the size of a shield dimension, as commonly assumed by all researchers and shield capacity is not a fixed property for a longwall panel or a mine or a coal seam. A new mechanism on the interaction between shield's hydraulic leg pressure and roof strata for shield loading is proposed.
基金the National Natural Science Foundation of China (No. 51304208)the Science and Technology Research of the Ministry of Education of China
文摘In order to study the strength-weakening law of roofs of water-rich roadway, this study used FLAC software, and simulated and analyzed the failure characteristics of the surrounding rock of water-rich roadway under the condition of different cross sections and support parameters, finally obtained the stress distribution of the principle stress of the roadway as well as the displacement variation of its surrounding rock. Results indicate that the roof stability of roadway with semicircular cross section is better than the roadway with inclined rectangular cross section under water-rich condition. Besides, the surrounding rock deformation of roadway under the action of water shows a pronounced increase compared to the roadway without the action of water due to the fact that water will obviously weaken the surrounding rock of roadway, especially its roof. It is very beneficial to control roof stability of water-rich roadway and guarantee the roadway stability during its service life by improving the pretension of bolt and cable as well as decreasing inter-row spacing of the bolt.
文摘A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a dielectric barrier discharge actuator is modeled with a phenomenological method for plasma simulation coupled with the compressible Navier-Stokes equations. The governing equations are solved using an efficient implicit finitevolume method. The responses of the separated flow field to the effects of an unsteady body force in various inter- pulses and duty cycles as well as different locations and magnitudes are studied. It is shown that the duty cycle and inter-pulse are key parameters for flow separation control. Additionally, it is concluded that the body force is able to attach the flow and can affect boundary layer grow that Mach number 0.1 and Reynolds number of 45000.
文摘A novel distributed numerical control (DNC) integrated system based on plug-in software technology is proposed. It connects new or old numerical control (NC) machine tools which have inhomogeneous numerical control systems with CAD/CAM system by CANbus network. A DNC computer is able to control 15 sets of NC machine tools reliably at the same time. The novel DNC system increases the efficiency of machine tools and improve the production management level by realizing non-paper production, agile manufacturing, networked manufacturing and so on in the near future. Key technologies to construct the novel DNC integrated system include the integration of inhomogeneous numerical control systems, NC program restart, and algorithm for communication competition. Such system has demonstrated successful applications in some corporations that have acquired good economic benefits and social effects.
基金Project supported by the National Natural Science Foundation of China(Grant No.11672135)a Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.201461)
文摘Based on the Fourier–Chebyshev spectral method, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with direct numerical simulation(DNS) methods for different Reynolds numbers. A formula is derived to express the relation between fluctuating velocities and the friction drag coefficient. With the application of electromagnetic force, the in-depth relations among the fluctuating velocities near the wall, Reynolds stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The fluctuating velocities along the streamwise and normal directions are suppressed significantly,while the fluctuating velocity along the spanwise direction is enhanced dramatically due to the spanwise electromagnetic force. However, the values of Reynolds stress depend on the fluctuating velocities along the streamwise and normal directions rather than that along the spanwise direction. Therefore, the significant effect of drag reduction is obtained. Moreover,the maximum drag reduction is weakened due to the decay of control effect for fluctuating velocities as the Reynolds number increases.
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
文摘This paper investigates the synchronization of a fractional order hyperchaotic system using passive control. A passive controller is designed, based on the properties of a passive system. Then the synchronization between two fractional order hyperchaotic systems under different initial conditions is realized, on the basis of the stability theorem for fractional order systems. Numerical simulations and circuitry simulations are presented to verify the analytical results.
基金Supported by the National Key Laboratory of Vehicular Transmission (9140C3405020905)the National Natural Science Foundation of China(50905016)
文摘To obtain the performance characteristics of hydrodynamic tractor-retarder assembly under traction work condition,a numerical simulation model of flow channel was established and tetrahedron unstructured grids were adopted in the meshing stage.The racing rotating speed of the brake wheels was calculated by computational fluid dynamics（CFD） calculation and interpolation,and then accurate boundary condition was applied to the CFD simulation to study the pressure and velocity distribution of internal flow field in hydrodynamic tractor-retarder assembly.Finally,the original characteristics were calculated by CFD post-processing analysis.Comparison of experimental data and flow field analysis results showed that the calculation tolerance of the torque ratio K and the efficiency η was less than 5%,and the calculation tolerance of the pump torque coefficient λ was less than 10%.
基金Foundation item： Supported by Supported by the National Natural Science Foundation of China （Grant No. 51009070）.
文摘In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104〈Re〈1.54×106. The calculations were performed by means of solving the 2-D Unsteady Reynolds-Averaged Navier-Stokes （URANS） equations with a k-ε turbulence model. The calculated results, produced flow structure drag and lift coefficients, as well as Strouhal numbers. The findings were in good agreement with previous published data, which also supplied us with a good understanding of the flow across cylinders of different high Reynolds numbers. Meanwhile, an effective measure was presented to control the lift force on a cylinder, which points the way to decrease the vortex induced vibration of marine structure in future.
基金supported by the National HighTechnology Research and Development Program of China(863 Program)(2007AA06Z214)"Taishan Scholars"Construction Project(No.ts20070704).
文摘Gelled particles can be transferred deeply inside oil reservoirs to block water channels due to their physicochemical characteristics, including swelling, deformation, and synergetic effect （reacting with polymers）, and then the injection profiles are significantly modified. At present, research on gelled particles is mainly focused on laboratory studies of drive mechanisms, and rarely on mathematical models describing the blocking process of gelled particles. In this paper, the blocking process of gelled particles is divided into two sub-processes： deposition and desorption due to particle deformation. A mathematical model based on filtration theory is proposed considering the effect of characteristics of gelled particles on the blocking process. Blocking laws were simulated and researched using the mathematical model. Results of the simulation of the blocking of gelled particles are quite consistent with the experimental results, which confirms the reliability of the mathematical model developed.
基金National Natural Science Foundation of China(No.61971345)the Foundation for Key Laboratories of National Defense Science and Technology of China(No.614220120030810).
文摘The primary issue regarding the plasma synthetic jet actuator(PSJA)is its performance attenuation at high frequencies.To solve this issue,a self-supplementing,dual-cavity,plasma synthetic jet actuator(SD-PSJA)is designed,and the static properties of the SD-PSJA are investigated through experiments and numerical simulations.The pressure measurement shows that the SD-PSJA has two saturation frequencies(1200 Hz and 2100 Hz),and the experimental results show that both the saturation frequencies decrease as the volume of the bottom cavity of the SD-PSJA increases.As the size of the supplement hole increases,the first saturation frequency increases continuously,while the second saturation frequency shows a trend of first decreasing and then increasing.Numerical simulations show that the working process of the SD-PSJA is similar to that of the PSJA,but the volume of the cavity in the SD-PSJA is smaller than that of the PSJA;the SD-PSJA can supplement air to the top cavity through two holes,thus reducing the refresh time and effectively improving the jet intensity of the actuator at high frequencies.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
