In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline--online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented.

翻译：本文提出了一种基于预求解模块化装配的新型工程系统参数化代理模型构建方法。每个模块均为考虑参数化几何、材料及边界条件的通用参数化解。通过装配这些模块并满足界面连续性约束，可获得完整问题的参数化代理模型。本文采用与NURBS几何表示相结合的PGD技术为每个模块创建参数化模型。在该技术中，NURBS对象可将参数化非规则域上的边界值问题映射至规则参考域，而PGD用于在参考域中建立降阶模型。在装配阶段，通过求解优化问题实现界面连续性约束的满足。所提方法基于离线-在线计算范式：离线阶段构建多个预求解模块，在线阶段可近乎实时地完成模块装配，从而快速评估系统整体响应。为展示该方法潜力，本文给出了热传导与板弯曲结构数值算例。