Level-Set Topology Optimization with PDE Generated Conformal Meshes

Watch a technical presentation from the 2024 MFEM Workshop exploring level-set topology optimization with PDE generated conformal meshes. Dive into how topology optimization can provide engineers with systematic computational tools for developing optimal designs, focusing on boundary and interface regions rather than traditional density-based approaches. Learn about a novel PDE-based level-set optimization method where geometries are described through iso-contours of level-set fields discretized over a mesh, with nodal heights serving as design parameters. Explore how the analysis mesh is morphed using the Target-Matrix Optimization Paradigm (TMOP) to conform with level-set field isocontours while maintaining mesh quality. Understand the implementation of this framework using MFEM, including design sensitivity calculations through adjoint approaches, and examine its application to two- and three-dimensional multi-material optimization problems in linear diffusion and elasticity. Discover the challenges and solutions related to mesh morphing, level-set regularization, and parallel computing considerations in this advanced computational approach.