This paper deals with the simulation of parametrized strongly-coupled multiphysics problems. The proposed method is based on previous works on multiphysics problems using the LATIN algorithm and the Proper Generalized Decomposition (PGD). Unlike conventional partitioning approaches, the LATIN-PGD solver applied to multiphysics problems builds the coupled solution by successively adding global corrections to each physics within an iterative procedure. The reduced-order bases for the different physics are built independently through a greedy algorithm, ensuring accuracy up to the desired level. This flexibility is used herein to efficiently handle parametrized problems, as it allows to enrich the bases independently along the variations of the parameters. The proposed approach is exemplified on several three-dimensional numerical examples in the case of thermo-mechanical coupling. We use a standard monolithic scheme to validate its accuracy. Our results highlight the adaptability of the proposed strategy to the coupling strength. Concerning the parametrized aspects, the method’s capability is illustrated through parametric studies with uncertain material parameters, resulting in significant performance gains over the monolithic scheme. Our observations suggest that the proposed computational strategy is effective and versatile when dealing with strongly-coupled multiphysics problems.

中文翻译：

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用于解决参数化强耦合热机械问题的模块化模型降阶方法


本文涉及参数化强耦合多物理场问题的仿真。所提出的方法基于之前使用 LATIN 算法和适当广义分解 (PGD) 解决多物理问题的工作。与传统的划分方法不同，应用于多物理场问题的 LATIN-PGD 求解器通过在迭代过程中连续向每个物理场添加全局校正来构建耦合解决方案。不同物理场的降阶基础是通过贪婪算法独立构建的，确保精度达到所需的水平。本文使用这种灵活性来有效地处理参数化问题，因为它允许沿着参数的变化独立地丰富基础。所提出的方法在热机耦合情况下的几个三维数值示例中得到了例证。我们使用标准的整体方案来验证其准确性。我们的结果强调了所提出的策略对耦合强度的适应性。关于参数化方面，该方法的能力通过不确定材料参数的参数研究来说明，从而比整体方案获得显着的性能提升。我们的观察表明，在处理强耦合多物理场问题时，所提出的计算策略是有效且通用的。