Variational Minimization Formulation for Phase-Field Topology Optimization and Coupled Problems

Explore a rigorous mathematical framework for variational minimization formulations in this 22-minute conference talk from FerriteCon 2025. Learn about a two-field canonical minimization formulation that supports phase-field approaches to topology optimization and extends naturally to other coupled problems such as second-order poro-elasticity models used to capture hydro-mechanical behavior in porous media. Discover how this formulation emphasizes balancing multiple interacting fields in a unified energy minimization setting, a common strategy in gradient-based continuum theories. Gain practical insights into using Ferrite.jl for teaching computational mechanics courses and research workflows through the speaker's experience as both an instructor and institute IT administrator. Master finite element formulations, variational methods in multiphysics problems, phase-field modeling, and the integration of modern numerical techniques within Julia's scientific ecosystem.