一种充分局部化的子结构并行有限元方法的变分原理

Variation Principle for the Localized FETI Method

局部化的有限元分裂内联法(以下简称L-FETI),是一种适合于机群系统的并行有限元方法,它将一个连续结构系统分解为多个独立的子域,各子域之间通过分区框架实现耦合。本文将分区框架视为无体积、无惯性的独立连接结构,在区域分解界面上引入局部化的界面位移和界面内力,直接从能量原理出发,构造了分区系统的势能泛函,完成了L-FETI方法的变分格式推导,说明了L-FETI方法在处理区域网格匹配问题和区域网格不匹配问题时所具有的一致性并引入惯性力,导出了基于L-FETI方法的动力学方程。

The localized finite element tearing and interconnecting （L-FETI） method divides a continuous structural system into several independent subdomains which are interconnected by a partition frame. The partition frame, in our opinion, is an independent and connecting structure with zero volume and zero inertia. We introduce the subdomain partition interface to the localized interface displacement and interface internal force, Starting directly from the energy principle we construct generalized potential energy functions, complete the derivation of the varia- tional equations for the L-FETI method and explain the consistency of the L-FETI method in treating the problems of subdomain mesh matching and subdomain mesh non-matching. Finally we introduce inertia force and derive the dynamic equations based on the L-FETI method.