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A fictitious domain decomposition method for a nonlinear bonded structure
Mathematics and Computers in Simulation ( IF 4.6 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.matcom.2020.09.003
Amina Chorfi , Jonas Koko , Olivier Bodart

Abstract We study a fictitious domain decomposition method for a nonlinearly bonded structure. Starting with a strongly convex unconstrained minimization problem, we introduce an interface unknown such that the displacement problems on each subdomain become uncoupled in the saddle-point equations. The interface unknown is eliminated and a Uzawa conjugate gradient domain decomposition method is derived from the saddle-point equations of the stabilized Lagrangian functional. To avoid interface fitted meshes we use a fictitious domain approach, inspired by XFEM, which consists in cutting the finite element basis functions around the interface. Some numerical experiments are proposed to illustrate the efficiency of the proposed method.

中文翻译:

非线性键合结构的虚拟域分解方法

摘要 我们研究了非线性键合结构的虚拟域分解方法。从一个强凸无约束最小化问题开始,我们引入了一个未知接口,使得每个子域上的位移问题在鞍点方程中变得解耦。消除了未知界面,并从稳定拉格朗日泛函的鞍点方程导出了 Uzawa 共轭梯度域分解方法。为了避免界面拟合网格,我们使用了一种受 XFEM 启发的虚拟域方法,该方法包括切割界面周围的有限元基函数。提出了一些数值实验来说明所提出方法的有效性。
更新日期:2020-09-01
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