标题： 基于分层误差估计的参数化组件非线性系统在线自适应超降阶减基单元方法 显示英文标题

标题： An online-adaptive hyperreduced reduced basis element method for parameterized component-based nonlinear systems using hierarchical error estimation

摘要： 我们提出了一种在线自适应超降阶减基单元方法，用于参数化、基于组件的非线性系统的模型降阶。 该方法在离线阶段准备一个包含不同保真度水平的超降阶原型组件库，在在线阶段使用实例化组件组装目标系统，其保真度根据用户指定的系统级误差容限进行自适应选择。 为了实现这一点，我们引入了一个分层误差估计框架，该框架比较不同保真度水平下的解，并基于组件级误差指示器驱动局部细化策略。 我们还提供了一个高效的系统级误差估计器，以确保自适应策略满足所需的精度。 组件级的超降阶通过经验求积过程进行，训练精度由Brezzi--Rappaz--Raviart定理指导。 所提出的方法在一个包含最多225个组件和68个参数的非线性热鳍系统家族中进行了演示。 数值结果表明，与真实有限元模型相比，超降阶基单元模型在1%的误差水平下实现了O(100)的计算量减少。 此外，自适应细化策略通过选择性地丰富具有较高局部误差的组件，提供了比均匀细化更有效的误差控制。 显示英文摘要

摘要： We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components of various fidelity levels and, in the online phase, assembles the target system using instantiated components whose fidelity is adaptively selected to satisfy a user-prescribed system-level error tolerance. To achieve this, we introduce a hierarchical error estimation framework that compares solutions at successive fidelity levels and drives a local refinement strategy based on component-wise error indicators. We also provide an efficient estimator for the system-level error to ensure that the adaptive strategy meets the desired accuracy. Component-wise hyperreduction is performed using an empirical quadrature procedure, with the training accuracy guided by the Brezzi--Rappaz--Raviart theorem. The proposed method is demonstrated on a family of nonlinear thermal fin systems comprising up to 225 components and 68 parameters. Numerical results show that the hyperreduced basis element model achieves O(100) computational reduction at 1% error level relative to the truth finite-element model. In addition, the adaptive refinement strategy provides more effective error control than uniform refinement by selectively enriching components with higher local errors.