Quasicontinuum Coupling for a Field-Based Interaction Potential
Quasicontinuum Coupling for a Field-Based Interaction Potential
复制标题
基于场的相互作用势的准连续耦合
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
E. Süli
中科院分区：
文献类型：
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作者：
B. Langwallner;C. Ortner;E. Süli
我们考虑通过最小化问题给出的一维原子相互作用势，这产生了一个场。在这种情况下，原子上的力由涉及该场的局部表达式给出。该模型的一个便利特征是存在力的弱公式，这为与连续介质模型的耦合提供了自然的连接点。我们建议基于将域分解为原子区域和连续区域的类准连续耦合机制。在连续统区域中，我们使用基于柯西玻恩规则的近似。在原子子域中，应用具有狄利克雷边界条件的原子模型的版本。必须特别注意原子子问题对边界和边界条件的依赖性。应用非线性分析的概念，我们展示了拟连续谱近似解的存在性和收敛性。
We consider an atomistic interaction potential in one dimension given through a minimization problem, which gives rise to a field. The forces on atoms are in this case given by local expressions involving this field. A convenient feature of this model is the existence of a weak formulation for the forces, which provides a natural connection point for the coupling with a continuum model. We suggest Quasicontinuum-like coupling mechanisms that are based on a decomposition of the domain into an atomistic and a continuum region. In the continuum region we use an approximation based on the Cauchy–Born rule. In the atomistic subdomain a version of the atomistic model with Dirichlet boundary conditions is applied. Special attention has to be paid to the dependence of the atomistic subproblem on the boundary and the boundary conditions. Applying concepts from nonlinear analysis we show existence and convergence of solutions to the Quasicontinuum approximation.