参数解涉及几何与计算机辅助设计的集成
Parametric solutions involving geometry integrated with computer-aided design
AI总结：
本文提出了一种通用方法，用于计算描述领域几何参数集的离线解，能够处理不同几何参数值的信息并计算灵敏度，通过NURBS定义几何，结合CAD预处理程序，利用PGD方法克服维度灾难，并展示了不可压缩流体的最优收敛率。
摘要：
本文的主要目标是描述一种通用且原创的方法，用于计算描述领域几何参数集的离线解。即，一种能够包含不同几何参数值信息并允许快速计算灵敏度的解。不同于问题依赖的方法，本文为标准工程环境提供了一个通用框架，其中几何由NURBS定义。现在，控制几何的参数是定义NURBS曲线或曲面的控制点。本文提出的方法适用于2D和3D场景，能够无缝集成到CAD预处理程序中。此处应用的适当通用分解（PGD）用于计算显式几何参数化的解，从而克服维度灾难。此外，展示了PGD对不可压缩流体的最优收敛率。
英文摘要：
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
