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：本文提出一种通过扩展标准贴体策略至任意形状单元剖分，使多边形网格适配水平集函数零等值线的修正方法。该新型水平集适配方法与间断伽辽金有限元逼近相结合，能够有效规避网格质量后处理环节，为模拟含内嵌或演化复杂几何特征的物理问题提供了理想框架。首先通过线弹性方程验证方法在处理异质材料属性构型时的逼近能力，进而将水平集适配方法与最小柔度拓扑优化技术融合，获得边界清晰且力学性能可靠的优化布局。大量数值实验证实了该方法的有效性。