论文标题
基于PDE的参数化技术在基于梯度的IgA形状优化应用中的作用
The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications
论文作者
论文摘要
本文提出了一种基于等几何分析原理（IGA）的形状优化算法，其中几何学的参数化作为附加的PDE-constraint进入问题表述。受IGA的等载原理的启发，使用相同的数值技术处理参数化和管理状态方程。这导致了一个相对易于区分的方案，从而使梯度和后续梯度的优化完全符号衍生。为了提高计划的效率和鲁棒性，在每次优化迭代期间都重新选择了基础，并根据当前需求进行了调整。该方案在两个测试用例中得到了验证。
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases.
