General treatment of essential boundary conditions in reduced order models for non-linear problems
General treatment of essential boundary conditions in reduced order models for non-linear problems
复制标题
非线性问题降阶模型中基本边界条件的一般处理
DOI：
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发表时间：
2016
影响因子：
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通讯作者：
S. Idelsohn
中科院分区：
文献类型：
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作者：
Alejandro Cosimo;A. Cardona;S. Idelsohn
在非线性问题的降阶模型（ROMs）中，非齐次基本边界条件必须仔细处理。为了研究这个问题，分析了两种方法：一种是强边界条件的方法，另一种是弱边界条件的方法。在这项工作中提出的想法适用于后验rom的大领域。然而，为了处理与问题的非线性相关的代价，特别考虑了一种后验超约简方法。研究了具有温度相关热物理性质和时间相关基本边界条件的非线性瞬态热传导问题的应用。然而，在这项工作中引入的策略是普遍适用的。
Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this issue, two methods are analysed: one in which the boundary conditions are imposed in an strong way, and a second one in which a weak imposition of boundary conditions is made. The ideas presented in this work apply to the big realm of a posteriori ROMs. Nevertheless, an a posteriori hyper-reduction method is specifically considered in order to deal with the cost associated to the non-linearity of the problems. Applications to nonlinear transient heat conduction problems with temperature dependent thermophysical properties and time dependent essential boundary conditions are studied. However, the strategies introduced in this work are of general application.