2023/09/20 by Nicola Ferro, Stefano Micheletti, Ferro, Nicola +9
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Engineering #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Finance #Topology Optimization in Engineering #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2309.11389
openalex publication_date 2023/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.