学术报告

报告人:  Luigi Brugnano教授               

 意大利佛罗伦萨大学（Universita' degli Studi, Firenze）

报告题目: Line Integral Methods for Conservative Problems

报告摘要: Many problems deriving from applications are characterized by the presence of invariants/constants of motion. Usually, they concisely characterize relevant geometric properties of the corresponding solutions and, therefore, they are of great importance for the correct simulation of the underlying phenomena. For this reason, one usually speaks about “conservative problems”.

    In this framework, the so called “Geometric Integration” deals with the definition and study of numerical methods which are able to reproduce relevant geometric properties of the continuous dynamical system,  in the corresponding discrete dynamical systems generated by the methods.

     Hamiltonian problems constitute a relevant class of problems of this type, which are widely used in the modelling of very many phenomena, ranging from the nano-scale of molecular dynamics to the macro-scale of celestial mechanics. In fact, for such problems the corresponding Hamitonian function is conserved, and often it assumes the phisical role of total energy. Consequently, it is easily realized that its conservation is of paramount importance, for a correct long-term simulation of the phenomena. Methods able to conserve the Hamiltonian are, therefore, named “energy-conserving”.

    This lecture will be divided into the following five sections:

Section One:     A Primer on Line Integral Methods;

Section Two:     Examples of Hamiltonian Problems;

Section Three:   Analysis of Hamiltonian Boundary Value Methods;

Section Four: Implementing The Methods and Numerical Illustrations

Section Five:   Hamiltonian Partial Differential Equations.

We shall describe a class of energy-conserving methods based on a recently defined approach to the problem, relying on the so called “discrete line integral”. This results into a class of energy-conserving Runge-Kutta methods for Hamiltonian problems. Moreover, the approach can be easily extended to more general classes of conservative problems.

报告时间:  Section One: 2016年1月18日上午10：00-12：00

            Section Two: 2016年1月19日上午10：00-12：00

            Section Three: 2016年1月20日上午10：00-12：00

            Section Four: 2016年1月21日上午10：00-12：00

            Section Five: 2016年1月22日上午10：00-12：00

报告地点: 科技楼南楼702室