W24-01 Modeling, Discretization, Optimization, and Simulation of Phase-Field Fracture Problems

Instructor(s):  Thomas WIck, Leibniz University Hannover


This course is devoted to phase-field fracture methods. Four different sessions (each of 90 minutes) are centered around modeling, discretizations, solvers, adaptivity, optimization, simulations and current developments. The key focus is on research work and teaching materials concerned with the accurate, efficient and robust numerical modeling. These include relationships of model, discretization, and material parameters and their influence on discretizations and the nonlinear (Newton-type methods) and linear numerical solution. One application of such high-fidelity forward models is in optimal control, where a cost functional is minimized by controlling Neumann boundary conditions. Therein, as a side-project (which is itself novel), space-time phase-field fracture models have been developed and rigorously mathematically proved. Emphasis in the entire course is on a fruitful mixture of theory, algorithmic concepts and exercises. Besides these lecture notes, further materials are available, such as for instance the open-source libraries pfm-cracks and DOpElib. The prerequisites are lectures in continuum mechanics, introduction to numerical methods, finite elements, and numerical methods for ODEs and PDEs. In addition, functional analysis (FA) and theory of PDEs is helpful, but for most parts not necessarily mandatory. 


Instructor: Thomas Wick

Proposed schedule:

08:30 AM - 10:00 AM

Morning break

10:30 AM - 12:00 AM

Lunch break

01:00 PM - 02:30 PM

Afternoon break

03:00 PM - 04:30 PM