In the context of MOR techniques for parametrized PDEs, a novel computational method relying on NURBS-based geometric mappings and PGD-based space separated representations has recently been developed. Such approach has opened new perspectives to classical PGD formulations. In particular, it has extended the use of the PGD to complex non-separable an non-simply-connected domains. Moreover, the domain is approximated through NURBS-based shape functions whose control points are treated as problem extra coordinates into the PGD constructor, allowing the efficient computation of geometrically parametrized solutions. The aim of this paper is to suggest the use of the coupled NURBS-PGD method to solve a variety of engineering problems characterized by evolving domains and parametric shapes. Special attention is addressed to inverse identification and shape optimization.

在参数化偏微分方程的 MOR 技术背景下，最近开发了一种依赖于基于 NURBS 的几何映射和基于 PGD 的空间分离表示的新颖计算方法。这种方法为经典的 PGD 配方开辟了新的视角。特别是，它将 PGD 的使用扩展到复杂的不可分离的非简单连接的域。此外，该域通过基于 NURBS 的形状函数进行近似，其控制点被视为 PGD 构造函数中的问题额外坐标，从而可以有效计算几何参数化解决方案。本文的目的是建议使用耦合 NURBS-PGD 方法来解决以演化域和参数形状为特征的各种工程问题。