论文标题
PDE约束形状优化的空间映射
Space Mapping for PDE Constrained Shape Optimization
论文作者
论文摘要
空间映射技术用于有效解决复杂的优化问题。它结合了精细模型模拟的准确性与粗模型优化的速度，以近似良好模型优化问题的解决方案。在本文中，我们提出了新的空间映射方法，以解决由部分微分方程（PDE）约束的形状优化问题。我们在基于Steklov-Poincaré-type指标的Riemannian设置中介绍了这些方法，并讨论了其数值离散和实施。我们研究了空间映射方法在几个模型问题上的数值性能。我们的数值结果突出了方法解决复杂形状优化问题的极大效率。
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model optimization problem. In this paper, we propose novel space mapping methods for solving shape optimization problems constrained by partial differential equations (PDEs). We present the methods in a Riemannian setting based on Steklov-Poincaré-type metrics and discuss their numerical discretization and implementation. We investigate the numerical performance of the space mapping methods on several model problems. Our numerical results highlight the methods' great efficiency for solving complex shape optimization problems.
