A Dirichlet–Neumann type algorithm for contact problems with friction
A Dirichlet–Neumann type algorithm for contact problems with friction
复制标题
用于解决摩擦接触问题的 Dirichlet-Neumann 型算法
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
B. Wohlmuth
中科院分区：
文献类型：
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作者：
R. Krause;B. Wohlmuth
摘要：区域分解技术为偏微分方程组的数值逼近提供了强有力的工具。给出了线弹性体间有库仑摩擦的非线性接触问题数值解的一种新算法。非线性问题的离散化是基于迫击炮技术。我们使用对偶基拉格朗日乘子空间来耦合不同的物体。接触区域的边界数据传输是该算法的关键。它是由非匹配三角剖分上的迫击炮离散化产生的尺度质量矩阵实现的。我们使用非线性块Gauss-Seidel方法作为迭代求解器，这可以解释为求解非线性问题的Dirichlet-Neumann算法。在每一步迭代过程中，我们都要求解一个线性Neumann问题和一个非线性Snowini问题。用单调多重网格法实现了对西诺里尼问题的求解。数值结果说明了该方法在2D和3D中的性能。
Abstract.Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We introduce a new algorithm for the numerical solution of a nonlinear contact problem with Coulomb friction between linear elastic bodies. The discretization of the nonlinear problem is based on mortar techniques. We use a dual basis Lagrange multiplier space for the coupling of the different bodies. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from the mortar discretization on non-matching triangulations. We apply a nonlinear block Gauss–Seidel method as iterative solver which can be interpreted as a Dirichlet–Neumann algorithm for the nonlinear problem. In each iteration step, we have to solve a linear Neumann problem and a nonlinear Signorini problem. The solution of the Signorini problem is realized in terms of monotone multigrid methods. Numerical results illustrate the performance of our approach in 2D and 3D.