The level set and density methods for topology optimization are often perceived as two very different approaches. This has to some extent led to two competing research directions working in parallel with only little overlap and knowledge exchange. In this paper, we conjecture that this is a misconception and that the overlap and similarities are far greater than the differences. To verify this claim, we employ, without significant modifications, many of the base ingredients from the density method to construct a crisp interface level set optimization approach using a simple cut element method. That is, we use the same design field representation, the same projection filters, the same optimizer, and the same so-called robust approach as used in density-based optimization for length scale control. The only noticeable difference lies in the finite element and sensitivity analysis, here based on a cut element method, which provides an accurate tool to model arbitrary, crisp interfaces on a structured mesh based on the thresholding of a level set—or density—field. The presented work includes a heuristic hole generation scheme and we demonstrate the design approach on several numerical examples covering compliance minimization and a compliant force inverter. Finally, we provide our MATLAB code, downloadable from www.topopt.dtu.dk, to facilitate further extension of the proposed method to, e.g., multiphysics problems.

拓扑优化的水平集和密度方法通常被视为两种截然不同的方法。在某种程度上，这导致了两个相互竞争的研究方向同时进行，几乎没有重叠和知识交流。在本文中，我们推测这是一个误解，而且重叠和相似之处远大于差异。为了验证这一说法，我们采用了许多基本要素，而没有进行重大修改，而这些要素均来自密度方法，以使用简单的切割元素方法构造出清晰的界面水平集优化方法。也就是说，我们使用相同的设计字段表示，相同的投影滤镜，相同的优化器和相同的所谓“鲁棒性”方法，这些方法用于基于长度的控制的基于密度的优化中。唯一值得注意的区别在于有限元和灵敏度分析（此处基于“切割元素”方法），该方法提供了一种基于水平集（或密度）场的阈值对结构化网格上的任意清晰界面进行建模的准确工具。提出的工作包括启发式孔生成方案，并且我们在几个数值示例上论证了设计方法，这些示例涵盖了柔量最小化和柔量力逆变器。最后，我们提供了可从www.topopt.dtu.dk下载的MATLAB代码，以方便将所提出的方法进一步扩展到例如多物理场问题。提出的工作包括启发式孔生成方案，并且我们在几个数值示例上论证了设计方法，这些示例涵盖了柔量最小化和柔量力逆变器。最后，我们提供了可从www.topopt.dtu.dk下载的MATLAB代码，以方便将所提出的方法进一步扩展到例如多物理场问题。提出的工作包括启发式孔生成方案，并且我们在几个数值示例上论证了设计方法，这些示例涵盖了柔量最小化和柔量力逆变器。最后，我们提供了可从www.topopt.dtu.dk下载的MATLAB代码，以方便将所提出的方法进一步扩展到例如多物理场问题。