桥接本征正交分解方法和增广Newton-Krylov算法：一种求解高度非线性力学问题的自适应模型降阶方法
Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
摘要：
本文介绍了基于POD的模型降阶技术和经典的牛顿/克雷洛夫求解器之间的桥梁。这座桥是用来推导出一个有效的算法来纠正，“在飞行中”，高度非线性问题的降阶建模进行强烈的拓扑变化。损伤引发问题的解决和解决通过一个修正的超约化方法。结果表明，该算法可以显着提高降阶模型的相关性与合理的额外费用时，即使在强烈的拓扑变化。
英文摘要：
This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved.
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