The Research Of Energy-Preserving Methods For Charged-Particle Dynamics

In recent years,structure-preserving algorithms which play an important role in scientific and engineering calculation,have been received more and more attention from scholars and many developments have been made.The basic principle of designing numerical methods is that they can preserve the properties of the original system as much as possible,such as the symplectic or multi-symplectic structures,symmetry,energy preservation and dissipation.Many kinds of useful structure-preserving algorithms have been proposed on the basis of this idea.The thought of structure-preserving algorithms was first put forward by Prof.Kang Feng.This thesis will go on a further study on the energy-preserving methods for solving the charged-particle dynamics.Three efficient energy-preserving methods were proposed for solving this system.This thesis is organized as follows.Chapter 1 briefly introduces the basic contents and its current research status of the charged-particle dynamics.Chapter 2 proposes a second-order energy-preserving method for solving the charged-particle dynamics and analyses its symmetric conditions and energy-preserving property.Furthermore,the long time near conservation of the momentum for this new method is discussed.From the results of the numerical experiments,it can be clearly observed that the novel method is more efficient and it can exactly preserve the energy of charged-particle dynamics.Moreover,the long time momentum is conserved well over a long time.Chapter 3 constructs a kind of arbitrarily high-order energy-preserving methods on the basis of the Lagrange basis polynomials and proves that the novel methods are of arbitrary order.A numerical experiment is carried out to show that the new methods have good accuracy and preserve the energy very well.Chapter 4 investigates the charged-particle dynamics in a strong and constant mag-netic field.A class of continuous-stage energy-preserving exponential integrators are for-mulated by using the idea of continuous stage methods and exponential integrators.The symmetric conditions,energy-preserving conditions and order conditions are discussed and analysed.According to those conditions,a second-order and third-order continuous-stage energy-preserving method is constructed.The numerical results show that the effectiveness of the new methods.