论文标题
用于基于组件的模型还原的一击重叠施瓦茨方法：应用于非线性弹性
A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity
论文作者
论文摘要
我们建议基于重叠的子域的参数化非线性椭圆偏微分方程（PDE），建议基于组件的（CB）参数模型订单降低（PMOR）公式。我们的方法将其视为一个受约束的优化语句，该声明会惩罚组件界面的跳跃，但在每个局部子域中PDE的近似满意度。此外，该方法依赖于当地状态分解为端口组件（与内部边界的解决方案相关联）以及在端口上消失的气泡组件：由于气泡组件是由解决方案值在相应端口上唯一确定的，因此我们可以将约束的陈述重新塑造为最不可能的范围，这些陈述最少会读取套件，方法是逐渐固定的方法，方法是逐步解决方案，并且是一个不合理的问题。我们为二维新霍克非线性力学问题提供了彻底的数值研究，以验证我们的方法。我们进一步讨论了数学公式和\ emph {先验性}误差分析的线性强制性问题。
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs) based on overlapping subdomains. Our approach reads as a constrained optimization statement that penalizes the jump at the components' interfaces subject to the approximate satisfaction of the PDE in each local subdomain. Furthermore, the approach relies on the decomposition of the local states into a port component -- associated with the solution on interior boundaries -- and a bubble component that vanishes at ports: since the bubble components are uniquely determined by the solution value at the corresponding port, we can recast the constrained optimization statement into an unconstrained statement, which reads as a nonlinear least-squares problem and can be solved using the Gauss-Newton method. We present thorough numerical investigations for a two-dimensional neo-Hookean nonlinear mechanics problem to validate our method; we further discuss the well-posedness of the mathematical formulation and the \emph{a priori} error analysis for linear coercive problems.
