一种保持拓扑的水平集形状优化方法
A Topology-Preserving Level Set Method for Shape Optimization
AI总结：
针对带几何与拓扑约束的形状优化，提出对数障碍罚的水平集方法，通过惩罚约束获得近似最优解。
摘要：
经典水平集方法将未知几何边界表示为函数的零水平集，已被证明在求解形状优化问题中非常有效。本研究解决了在存在简单几何和拓扑约束时使用水平集表示的问题。我们提出一种对数障碍罚函数来强制执行约束，从而得到形状设计问题的近似解。
英文摘要：
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.
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