基于非线性扩张算子的网格保形算法optimization
Mesh quality preserving shape optimization using nonlinear extension operators
摘要：
在这篇文章中，我们提出了一种形状优化算法，它能够处理大的变形，同时保持高水平的网格质量。基于映射方法，我们引入了一个非线性扩张算子，它将边界控制与区域变形联系起来，保证了结果形状的可接受性。主要的重点是比较完善的方法，涉及线性椭圆算子的扩展和额外的非线性平流的影响，可达到的形状。最后讨论了如何降低该算法的计算复杂性。扩展算子的非线性的好处是证实了几个数值试验的情况下，固定的，不可压缩的Navier-Stokes流在2D和3D。
英文摘要：
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.
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