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implicit Quadrature-Free Direct Reconstruction method for Efficient Scale-Resolving Simulations

Communications in Computational Physics 2023年第4期33卷 992-1034页

作者： Hojun You Juhyun Kim Chongam Kim Department of Aerospace System Engineering Sejong UniversitySeoul 05006Republic of Korea Department of Aerospace Engineering Seoul National UniversitySeoul 08826Republic of Korea Institute ofAdvanced Aerospace Technology SeoulNationalUniversitySeoul 08826Republic of Korea

The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved *** methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and *** physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on *** using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations *** address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG *** this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing *** DRM operator is applied to the residual computation in the matrix-free *** DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and ***,the A-stable Rosenbrock-type runge–kutta methods are adopted to achieve high-order accuracy in *** verification and validation from the manufactured solution to implicit large eddy simulations are *** computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.

关键词： Direct reconstruction method implicit runge-kutta method quadrature-free method discontinuous Galerkin method implicit large eddy simulation high performance computing

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implicit Integration with Adjoint Sensitivity Propagation for Optimal Control Problems Involving Differential-Algebraic Equations

Implicit Integration with Adjoint Sensitivity Propagation fo...

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第36届中国控制会议

作者： Canghua Jiang Kun Xie Zhiqiang Guo Kok Lay Teo School of Electrical Engineering and Automation Hefei University of Technology Department of Mathematics and Statistics Curtin University

ISBN: (纸本)9781538629185

For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then,adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.

关键词： Differential-algebraic equation implicit runge-kutta method Adjoint sensitivity Optimal control Delta robot

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Accelerating the Advanced-Step NMPC by a Lifted implicit runge-kutta Integrator for Fast Embedded Applications

Accelerating the Advanced-Step NMPC by a Lifted Implicit Run...

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第三十九届中国控制会议

作者： Zhu Zhu Canghua Jiang Cheng Jin Zhiqiang Guo Zongqi Xu School of Electrical Engineering and Automation Hefei University of Technology Zhongxing Telecommunication Equipment(ZTE) Corporation China Railway Signal & Communication Research & Design Institute Group Co. Ltd.

In order to reduce computational delay, advanced-step nonlinear model predictive control（as NMPC） divides the on-line computation into two steps. In the first step, an optimal control problem with predicted initial state is solved. Then, the computed control action is corrected by sensitivity update in the second step once the measurement of state is available. Since sensitivity update is valid only for small perturbation, the steps for state prediction cannot be too many, and the time constraint for the computation of optimal control is still stringent. For fast embedded applications, this paper proposes to incorporate a lifted implicit runge-kutta（IRK） integrator in the scheme of asNMPC. The derived nonlinear program（NLP） is thus small and dense, and can be solved without resorting to sparse linear algebra solver. Furthermore, this integrator requires fewer Newton iterations, and possesses similar convergence property as the simultaneous collocation integrator originally used. Based on it, variational sensitivity propagation is applied for gradient computation, which is decoupled from the integration of nominal equation, and thus has improved efficiency. This algorithm is implemented based on Ipopt with sIPOPT library. Warm start for primal and dual variables and the Hessian of the Lagrangian is also implemented. Numerical simulations on the control of a Delta robot demonstrate that the lifted IRK integrator can improve the computational efficiency of asNMPC considerably.

关键词： NMPC Differential-algebraic Equation implicit runge-kutta method Sensitivity Delta Robot

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