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Statements

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Extended finite element method 广义有限元方法 Méthode des éléments finis étendus
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Le concept d'Éléments Finis Étendus (X-FEM) a été introduit pour tenir compte des problèmes de convergence des éléments finis près d'éventuelles singularités du domaine. 广义有限元方法(英語:Generalized Finite Element Method,GFEM),是基于传统有限元方法(FEM)的一种数值分析方法,能够更加优雅、准确地解决材料交界面和断裂力学等非连续问题。这类问题在划分单元网格时,应用传统有限元方法往往需要使网格边界与非连续界面尽可能重合,带来极大的网格依赖(mesh-dependence)。对于复杂边界问题及形状变化问题(例如和裂纹扩展等),传统有限元需要花费大量的时间建立单元网格以及重建网格,同时还需要引入计算量处理裂尖端(crack tips)来避免奇异刚性矩阵。广义有限元正是在这样的背景下诞生,它对传统有限元的形函数(shape functions)进行扩展,在包含非连续的单元网格内使用强化方程(enrichment functions),来准确模拟非连续的物理场,这种方法又可称为扩展有限元(extended finite element method,XFEM)。 The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite element method (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions.
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广义有限元方法(英語:Generalized Finite Element Method,GFEM),是基于传统有限元方法(FEM)的一种数值分析方法,能够更加优雅、准确地解决材料交界面和断裂力学等非连续问题。这类问题在划分单元网格时,应用传统有限元方法往往需要使网格边界与非连续界面尽可能重合,带来极大的网格依赖(mesh-dependence)。对于复杂边界问题及形状变化问题(例如和裂纹扩展等),传统有限元需要花费大量的时间建立单元网格以及重建网格,同时还需要引入计算量处理裂尖端(crack tips)来避免奇异刚性矩阵。广义有限元正是在这样的背景下诞生,它对传统有限元的形函数(shape functions)进行扩展,在包含非连续的单元网格内使用强化方程(enrichment functions),来准确模拟非连续的物理场,这种方法又可称为扩展有限元(extended finite element method,XFEM)。 The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite element method (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions. Le concept d'Éléments Finis Étendus (X-FEM) a été introduit pour tenir compte des problèmes de convergence des éléments finis près d'éventuelles singularités du domaine.
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