Projected Runge-Kutta methods for constrained Hamiltonian systems  

作　　者：Yi WEI Zichen DENG Qingjun LI Bo WANG 

机构地区：[1]Department of Applied Mathematics,Northwestern Polytechnical University [2]Department of Engineering Mechanics,Northwestern Polytechnical University [3]Mechanical and Aerospace Engineering,Oklahoma State University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第8期1077-1094,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.11432010);the Doctoral Program Foundation of Education Ministry of China(No.20126102110023);the 111Project of China(No.B07050);the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001);the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)

摘　　要：Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

关 键 词：projected Runge-Kutta （R-K） method differential-algebraic equation（DAE） constrained Hamiltonian system energy and constraint preservation constraint violation 

分 类 号：O241.8[理学—计算数学]