A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th...A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.展开更多
This paper synchronizes control theory with computer vision by formalizing object tracking as a sequential decision-making process.A reinforcement learning(RL)agent successfully tracks an interface between two liquids...This paper synchronizes control theory with computer vision by formalizing object tracking as a sequential decision-making process.A reinforcement learning(RL)agent successfully tracks an interface between two liquids,which is often a critical variable to track in many chemical,petrochemical,metallurgical,and oil industries.This method utilizes less than 100 images for creating an environment,from which the agent generates its own data without the need for expert knowledge.Unlike supervised learning(SL)methods that rely on a huge number of parameters,this approach requires far fewer parameters,which naturally reduces its maintenance cost.Besides its frugal nature,the agent is robust to environmental uncertainties such as occlusion,intensity changes,and excessive noise.From a closed-loop control context,an interface location-based deviation is chosen as the optimization goal during training.The methodology showcases RL for real-time object-tracking applications in the oil sands industry.Along with a presentation of the interface tracking problem,this paper provides a detailed review of one of the most effective RL methodologies:actor–critic policy.展开更多
This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using...This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using the elliptic Ritz\|Volterra projection,the analysis of the error estimates for the finite element numerical solutions and the optimal H \+1\|norm error estimate are demonstrated.展开更多
In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear supe...In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition(POD). Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.展开更多
We study a new trust region affine scaling method for general bound constrained optimiza- tion problems. At each iteration, we compute two trial steps. We compute one along some direction obtained by solving an approp...We study a new trust region affine scaling method for general bound constrained optimiza- tion problems. At each iteration, we compute two trial steps. We compute one along some direction obtained by solving an appropriate quadratic model in an ellipsoidal region. This region is defined by an affine scaling technique. It depends on both the distances of current iterate to boundaries and the trust region radius. For convergence and avoiding iterations trapped around nonstationary points, an auxiliary step is defined along some newly defined approximate projected gradient. By choosing the one which achieves more reduction of the quadratic model from the two above steps as the trial step to generate next iterate, we prove that the iterates generated by the new algorithm are not bounded away from stationary points. And also assuming that the second-order sufficient condition holds at some nondegenerate stationary point, we prove the Q-linear convergence of the objective function values. Preliminary numerical experience for problems with bound constraints from the CUTEr collection is also reported.展开更多
The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangi...The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid.It is well known that some versions of the IB method can suffer from poor volume conservation.Methods have been introduced to improve the volume-conservation properties of the IB method,but they either have been fairly specialized,or have used complex,nonstandard Eulerian finite-difference discretizations.In this paper,we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method.We consider both collocated and staggered-grid discretization methods.For the tests considered herein,the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods,and in many cases considered in this work,the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes.We also compare the performance of cell-centered schemes that use either exact or approximate projection methods.We find that the volumeconservation properties of approximate projection IB methods depend strongly on the formulation of the projection method.When used with the IB method,we find that pressure-free approximate projection methods can yield extremely poor volume conservation,whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.展开更多
基金This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada(Grant OGPIN-336)and by the"Ministere de l'Education du Quebec"(FCAR Grant-ER-0725)
文摘A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.
文摘This paper synchronizes control theory with computer vision by formalizing object tracking as a sequential decision-making process.A reinforcement learning(RL)agent successfully tracks an interface between two liquids,which is often a critical variable to track in many chemical,petrochemical,metallurgical,and oil industries.This method utilizes less than 100 images for creating an environment,from which the agent generates its own data without the need for expert knowledge.Unlike supervised learning(SL)methods that rely on a huge number of parameters,this approach requires far fewer parameters,which naturally reduces its maintenance cost.Besides its frugal nature,the agent is robust to environmental uncertainties such as occlusion,intensity changes,and excessive noise.From a closed-loop control context,an interface location-based deviation is chosen as the optimization goal during training.The methodology showcases RL for real-time object-tracking applications in the oil sands industry.Along with a presentation of the interface tracking problem,this paper provides a detailed review of one of the most effective RL methodologies:actor–critic policy.
文摘This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using the elliptic Ritz\|Volterra projection,the analysis of the error estimates for the finite element numerical solutions and the optimal H \+1\|norm error estimate are demonstrated.
基金supported by the National Basic Research Program of China(No.2014CB744804)
文摘In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition(POD). Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.
基金Supported by NSFC(Grant Nos.10831006and11021101)CAS(Grant No.kjcx-yw-s7)
文摘We study a new trust region affine scaling method for general bound constrained optimiza- tion problems. At each iteration, we compute two trial steps. We compute one along some direction obtained by solving an appropriate quadratic model in an ellipsoidal region. This region is defined by an affine scaling technique. It depends on both the distances of current iterate to boundaries and the trust region radius. For convergence and avoiding iterations trapped around nonstationary points, an auxiliary step is defined along some newly defined approximate projected gradient. By choosing the one which achieves more reduction of the quadratic model from the two above steps as the trial step to generate next iterate, we prove that the iterates generated by the new algorithm are not bounded away from stationary points. And also assuming that the second-order sufficient condition holds at some nondegenerate stationary point, we prove the Q-linear convergence of the objective function values. Preliminary numerical experience for problems with bound constraints from the CUTEr collection is also reported.
基金support from American Heart Association grant 10SDG4320049National Science Foundation grants DMS 1016554 and OCI 1047734.
文摘The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid.It is well known that some versions of the IB method can suffer from poor volume conservation.Methods have been introduced to improve the volume-conservation properties of the IB method,but they either have been fairly specialized,or have used complex,nonstandard Eulerian finite-difference discretizations.In this paper,we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method.We consider both collocated and staggered-grid discretization methods.For the tests considered herein,the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods,and in many cases considered in this work,the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes.We also compare the performance of cell-centered schemes that use either exact or approximate projection methods.We find that the volumeconservation properties of approximate projection IB methods depend strongly on the formulation of the projection method.When used with the IB method,we find that pressure-free approximate projection methods can yield extremely poor volume conservation,whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.