论文标题
使用非线性扩展运算符优化网格质量的形状
Mesh quality preserving shape optimization using nonlinear extension operators
论文作者
论文摘要
在本文中，我们提出了一种形状优化算法，该算法能够处理大型变形，同时保持高水平的网格质量。基于映射的方法，我们引入了一个非线性扩展运算符，该运算符将边界控制与域变形联系起来，以确保对产生形状的可接受性。主要重点是涉及线性纤维化算子扩展的良好方法之间的比较，以及其他非线性对流对一组可及形状的影响。此外，还讨论了如何降低所提出算法的计算复杂性。非线性在扩展运算符中的好处得到了几个数值测试案例，即2D和3D中的固定，不可压缩的Navier-Stokes流量。
In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings we introduce a nonlinear extension operator, which links a boundary control to domain deformations, ensuring admissibility of resulting shapes. The major focus is on comparisons between well-established approaches involving linear-elliptic operators for the extension and the effect of additional nonlinear advection on the set of reachable shapes. It is moreover discussed how the computational complexity of the proposed algorithm can be reduced. The benefit of the nonlinearity in the extension operator is substantiated by several numerical test cases of stationary, incompressible Navier-Stokes flows in 2d and 3d.
