We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routine...We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines:one hinges on Binev's algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy;the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying D?rfler marking and h refinement.展开更多
For the problem of free⁃floating space robot(FFSR)that the motion of manipulator will cause a large disturbance to the attitude of satellite,a path planning method based on hp⁃adaptive Gauss pseudospectral method(hp⁃A...For the problem of free⁃floating space robot(FFSR)that the motion of manipulator will cause a large disturbance to the attitude of satellite,a path planning method based on hp⁃adaptive Gauss pseudospectral method(hp⁃AGPM)is proposed in this paper.In this method,the minimum reaction torque acting on satellite is taken as the objective function,and the number of segments and the order of polynomial in each segment are determined adaptively to improve the accuracy and the efficiency of the solution.At the same time,the theoretical convergence of the designed method is innovatively proved to ensure that the solution of the discretized nonlinear programming(NLP)problem is the optimal solution to the original optimal problem.The simulation results of a planar two degree⁃of⁃freedom(2⁃DOF)space manipulator show that the proposed path planning method is more effective than the resolved acceleration control(RAC)method and the control variable parameterization(CVP)method,and is better than other pseudospectral methods both in computation speed and the number of collocation points.展开更多
We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusi...We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.展开更多
To make full use of expanded maneuverability and increased range,adaptive constrained on-board guidance technology is the key capability for a glide vehicle with a double-pulse rocket engine,especially under the requi...To make full use of expanded maneuverability and increased range,adaptive constrained on-board guidance technology is the key capability for a glide vehicle with a double-pulse rocket engine,especially under the requirements of desired target changing and on-line reconfigurable control and guidance.Based on the rapid footprint analysis,whether the new target is within the current footprint area is firstly judged.If not,the rocket engine ignites by the logic obtained from the analysis of optimal flight range by the method of hp-adaptive Gauss pseudospectral method(hp-GPM).Then,an on-board trajectory generation method based on powered quasi-equilibrium glide condition(QEGC)and linear quadratic regulator(LQR)method is used to guide the vehicle to the new target.The effectiveness of the guidance method consisted of powered on-board trajectory generation,LQR trajectory tracking,footprint calculation,and ignition time determination is indicated by some simulation examples.展开更多
In this paper,high-order Discontinuous Galerkin(DG)method is used to solve the two-dimensional Euler equations.A shock-capturing method based on the artificial viscosity technique is employed to handle physical discon...In this paper,high-order Discontinuous Galerkin(DG)method is used to solve the two-dimensional Euler equations.A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities.Numerical tests show that the shocks can be captured within one element even on very coarse grids.The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions.In order to obtain better shock resolution,a straightforward hp-adaptivity strategy is introduced,which is based on the high-order contribution calculated using hierarchical basis.Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.展开更多
In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a...In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates.Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities,edge singularities,and an engineering benchmark problem of Maxwell’s equations.The hp-adaptive methods show much better performance than the h-adaptive method.展开更多
文摘We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines:one hinges on Binev's algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy;the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying D?rfler marking and h refinement.
文摘For the problem of free⁃floating space robot(FFSR)that the motion of manipulator will cause a large disturbance to the attitude of satellite,a path planning method based on hp⁃adaptive Gauss pseudospectral method(hp⁃AGPM)is proposed in this paper.In this method,the minimum reaction torque acting on satellite is taken as the objective function,and the number of segments and the order of polynomial in each segment are determined adaptively to improve the accuracy and the efficiency of the solution.At the same time,the theoretical convergence of the designed method is innovatively proved to ensure that the solution of the discretized nonlinear programming(NLP)problem is the optimal solution to the original optimal problem.The simulation results of a planar two degree⁃of⁃freedom(2⁃DOF)space manipulator show that the proposed path planning method is more effective than the resolved acceleration control(RAC)method and the control variable parameterization(CVP)method,and is better than other pseudospectral methods both in computation speed and the number of collocation points.
基金Open Access funding enabled and organized by Projekt DEAL.
文摘We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.
基金supported by the National Natural Science Foundation of China(No.61403100)Fundamental Research Funds for the Central Universities(HIT.NSRIF.2015037)
文摘To make full use of expanded maneuverability and increased range,adaptive constrained on-board guidance technology is the key capability for a glide vehicle with a double-pulse rocket engine,especially under the requirements of desired target changing and on-line reconfigurable control and guidance.Based on the rapid footprint analysis,whether the new target is within the current footprint area is firstly judged.If not,the rocket engine ignites by the logic obtained from the analysis of optimal flight range by the method of hp-adaptive Gauss pseudospectral method(hp-GPM).Then,an on-board trajectory generation method based on powered quasi-equilibrium glide condition(QEGC)and linear quadratic regulator(LQR)method is used to guide the vehicle to the new target.The effectiveness of the guidance method consisted of powered on-board trajectory generation,LQR trajectory tracking,footprint calculation,and ignition time determination is indicated by some simulation examples.
基金the foundation of the National Natural Science Foundation of China(11272152)the Aeronautical Science Foundation of China(20101552018)。
文摘In this paper,high-order Discontinuous Galerkin(DG)method is used to solve the two-dimensional Euler equations.A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities.Numerical tests show that the shocks can be captured within one element even on very coarse grids.The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions.In order to obtain better shock resolution,a straightforward hp-adaptivity strategy is introduced,which is based on the high-order contribution calculated using hierarchical basis.Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.
基金supported in part by the National Basic Research Project under the grant 2011CB309703,by the Funds for Creative Research Groups of China(Grant No.11021101)by China NSF under the grant 60873177+2 种基金supported in part by China NSF under the grants 11031006 and 11171334by the Funds for Creative Research Groups of China(Grant No.11021101)by the National Magnetic Confinement Fusion Science Program(Grant No.2011GB105003).
文摘In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates.Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities,edge singularities,and an engineering benchmark problem of Maxwell’s equations.The hp-adaptive methods show much better performance than the h-adaptive method.