检索结果-南通市图书馆

structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

在线全文

学校读者我要写书评

暂无评论

Plasma Science and Technology 2024年第6期26卷 88-102页

作者：张若涵王正汹肖建元王丰 Key Laboratory of Materials Modification by Laser Ion and Electron BeamsSchool of PhysicsDalian University of TechnologyDalian 116024People’s Republic of China Department of Plasma Physics and Fusion Engineering University of Science and Technology of ChinaHefei 230026People’s Republic of China

The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

关键词： structure-preserving algorithm averaged vector field classical Pauli particle guiding center dynamics

structure-preserving algorithmS FOR DYNAMICAL SYSTEMS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2002年第6期20卷 619-626页

作者： Geng Sun (Institute of Mathematic, Academic Sinica) Institute of Mathematic Academic Sinica

Presents a study which examined the structure-preserving algorithms to phase space volume for linear dynamical systems. Preservation of phase space volume for source-free dynamical systems; Description of a volume-preserving scheme for linear system with canonical form; Information on structure-preserving schemes for linear dynamical systems.

关键词： structure-preserving algorithm phase space volume source-free dynamical system.

structure-preserving algorithms for autonomous Birkhoffian systems

在线全文

学校读者我要写书评

暂无评论

Journal of Beijing Institute of Technology 2012年第1期21卷 1-7页

作者：孔新雷吴惠彬梅凤翔 School of Science Beijing Institute of Technology School of Aerospace Engineering Beijing Institute of Technology

The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhofflan systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.

关键词： Birkhoffian system discrete Birkhoffian equations structure-preserving algorithm

structure-preserving algorithms for the Duffng equation

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2008年第10期17卷 3623-3628页

作者：冮铁强梅凤翔解加芳 Department of Mechanics Beijing Institute of Technology

In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, based on the gradient- Hamiltonian decomposition theory of vector fields, by using splitting methods, this paper constructs structure-preserving algorithms （SPAs） for the Duffing equation. Then, according to the Liouville formula, it proves that the Jacobian matrix determinants of the SPAs are equal to that of the exact flow of the Duffing equation. However, considering the explicit Runge Kutta methods, this paper finds that there is an error term of order p＋l for the Jacobian matrix determinants. The volume evolution law of a given region in phase space is discussed for different algorithms, respectively. As a result, the sum of Lyapunov exponents is exactly invariable for the SPAs proposed in this paper. Finally, through numerical experiments, relative norm errors and absolute energy errors of phase trajectories of the SPAs and the Heun method （a second-order Runge-Kutta method） are compared. Computational results illustrate that the SPAs are evidently better than the Heun method when e is small or equal to zero.

关键词： structure-preserving algorithm Duffing equation gradient-Hamiltonian decomposition Runge-Kutta method

A DISSIPATION-preserving INTEGRATOR FOR DAMPED OSCILLATORY HAMILTONIAN SYSTEMS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2022年第4期40卷 570-588页

作者： Wei Shi Kai Liu College of Mathematical Sciences Nanjing Tech UniversityNanjing 211816China School of Statistics and Data Science Nanjing Audit UniversityNanjing 210023China

In this paper,based on discrete gradient,a dissipation-preserving integrator for weakly dissipative perturbations of oscillatory Hamiltonian system is *** solution of this system is a damped nonlinear ***,lots of nonlinear oscillatory mechanical systems including frictional forces lend themselves to this *** new integrator gives a discrete analogue of the dissipation property of the original ***,since the integrator is based on the variation-of-constants formula for oscillatory systems,it preserves the oscillatory structure of the *** properties of the new integrator are *** convergence is analyzed for the implicit iterations based on the discrete gradient integrator,and it turns out that the convergence of the implicit iterations based on the new integrator is independent of k Mk,where M governs the main oscillation of the system and usually k Mk≫*** significant property shows that a larger stepsize can be chosen for the new schemes than that for the traditional discrete gradient integrators when applied to the oscillatory Hamiltonian *** experiments are carried out to show the effectiveness and efficiency of the new integrator in comparison with the traditional discrete gradient methods in the scientific literature。

关键词： Weakly dissipative systems Oscillatory systems structure-preserving algorithm Discrete gradient integrator Sine-Gordon equation Continuousα-Fermi-Pasta-Ulam system

A LINEARLY-IMPLICIT ENERGY-preserving algorithm FOR THE TWO-DIMENSIONAL SPACE-FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION BASED ON THE SAV APPROACH

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2023年第5期41卷 797-816页

作者： Yayun Fu Wenjun Cai Yushun Wang School of Science Xuchang UniversityXuchang 461000China Jiangsu Key Laboratory for NSLSCS Jiangsu Collaborative Innovation Center of Biomedial Functional MaterialsSchool of Mathematical SciencesNanjing Normal UniversityNanjing 210023China

The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger ***,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar ***,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space *** that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete *** expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time ***,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.

关键词： Fractional nonlinear Schrodinger equation Hamiltonian system Scalar auxiliary variable approach structure-preserving algorithm

A LINEARLY-IMPLICIT structure-preserving EXPONENTIAL TIME DIFFERENCING SCHEME FOR HAMILTONIAN PDEs

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2024年第4期42卷 1063-1079页

作者： Yayun Fu Dongdong Hu Wenjun Cai Yushun Wang Henan Joint International Research Laboratory of High Performance Computation for Complex Systems School of ScienceXuchang UniversityXuchang 461000China School of Mathematics and Statistics Jiangxi Normal UniversityJiangxiNanchang 330022China Jiangsu Key Laboratory for NSLSCS Jiangsu Collaborative Innovation Center of Biomedial Functional MaterialsSchool of Mathematical SciencesNanjing Normal UniversityNanjing 210023China

In the paper,we propose a novel linearly implicit structure-preserving algorithm,which is derived by combing the invariant energy quadratization approach with the exponential time differencing method,to construct efficient and accurate time discretization scheme for a large class of Hamiltonian partial differential equations(PDEs).The proposed scheme is a linear system,and can be solved more efficient than the original energy-preserving ex-ponential integrator scheme which usually needs nonlinear *** experiments are performed to verify the conservation,efficiency and good performance at relatively large time step in long time computations.

关键词： structure-preserving algorithm Hamiltonian PDE Energy quadratization method Exponential time differencing

A LINEARLY-FITTED CONSERVATIVE （DISSIPATIVE） SCHEME FOR EFFICIENTLY SOLVING CONSERVATIVE （DISSIPATIVE） NONLINEAR WAVE PDES

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2017年第6期35卷 780-800页

作者： Kai Liu XinyuanWu Wei Shi College of Applied Mathematics Nanjing University of Finance ~ Economics Nanjing 210023 China Department of Mathematics Nanjing University State Key Laboratory for Novel Software Technology at Nanjing University Nanjing 210093 China College of Mathematical Sciences Nanjing Teeh University Nanjing 211816 China

The extended discrete gradient method is an extension of traditional discrete gradient method, which is specially designed to solve oscillatory Hamiltonian systems efficiently while preserving their energy exactly. In this paper, based on the extended discrete gradient method, we present an efficient approach to devising novel schemes for numerically solving conservative （dissipative） nonlinear wave partial differential equations. The new scheme can preserve the energy exactly for conservative wave equations. With a minor remedy to the extended discrete gradient method, the new scheme is applicable to dissipative wave equations. Moreover, it can preserve the dissipation structure for the dissipative wave equation as well. Another important property of the new scheme is that it is linearly-fitted, which guarantees much fast convergence for the fixed-point iteration which is required by an energy-preserving integrator. The efficiency of the new scheme is demonstrated by some numerical examples.

关键词： Conservative (dissipative) wave PDEs structure-preserving algorithm Linearly-fitted Average Vector Field formula Sine-Gordon equation.