Level Set Shape Optimization on Aggregated Polytopic Meshes

Explore level set shape optimization techniques using aggregated polytopic meshes in this 26-minute conference talk from the Workshop on "New perspective on Shape and Topology Optimization" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the challenges of determining optimal domain boundaries through the level set equation, also known as the Hamilton-Jacobi equation. Examine the evolution of structural optimization methods, from traditional finite difference approaches to the increasing use of Finite Element Methods. Discover a novel finite element method utilizing polytopic elements and a Discontinuous Galerkin scheme, designed to enhance boundary tracking accuracy and improve computational efficiency. Learn how this innovative approach addresses the limitations of standard conforming finite element methods in representing level set boundaries on given meshes.