We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in combination with a Discontinuous Galerkin finite element approximation, provides an ideal setting to model physical problems characterized by embedded or evolving complex geometries, since it allows skipping any mesh post-processing in terms of grid quality. The proposed methodology is firstly assessed on the linear elasticity equation, by verifying the approximation capability of the level set-fitted approach when dealing with configurations with heterogeneous material properties. Successively, we combine the level set-fitted methodology with a minimum compliance topology optimization technique, in order to deliver optimized layouts exhibiting crisp boundaries and reliable mechanical performances. An extensive numerical test campaign confirms the effectiveness of the proposed method.

翻译：我们提出一种方法，通过将标准体适应策略扩展到任意形状单元的网格剖分，来修改多边形网格以使其与水平集函数的零等值线相吻合。这种新颖的水平集适应方法，结合间断伽辽金有限元近似，为刻画具有嵌入或演变复杂几何特征的物理问题提供了理想环境，因为它可以避免任何关于网格质量的后期处理。该方法的性能首先在线弹性方程上进行评估，通过验证水平集适应方法在处理具有异质材料属性配置时的近似能力。随后，我们将水平集适应方法与最小柔度拓扑优化技术相结合，以提供具有清晰边界和可靠力学性能的优化布局。广泛的数值实验证实了所提方法的有效性。