计算力学中的现代数学方法的若干问题

Modern Mathematical Methods in Computational Mechanics

随着现代科学技术的高速发展 ,计算力学面临许多新课题 ,大范围非线性问题已成为计算力学研究的主攻方向 ,现代数学方法给计算力学的研究提供了强有力的工具。简要综述了计算力学所涉及的若干现代数学领域和方法 ,着重介绍了非线性问题的研究现状和发展 ,包括各类与现代数学密切相关的算法研究、Hamilton力学与辛几何、分叉理论等 ,以期展示现代数学方法在计算力学中的广泛应用。这些方法正在改变着计算力学研究的面貌 。

Along with the rapid development of modern science and technology,the computational mechanics is faced with a series of new problems.As a forceful tool,the modern mathematical methods are provided.In this paper,the domain of the modern mathematics and the methods related to the computational mechanics are briefly reviewed.Advances in nonliner problems are introduced.The topics include the various algorithms,Hamiltonian system and sympletic geometry,bifurcation theory,etc.The wide application of the modern mathematical methods to computational mechanics will bring about new changes in this field.