Modeling, Discretization, Optimization, and Simulation of PhaseField Fracture Problems

Thomas Wick

Leibniz University Hannover Institute of Applied Mathematics

Relevance to WCCM–ECCOMAS

This course has been delivered successfully at WCCM 2024 in Vancouver and in the GRK 2423 FRASCAL in Nov 2023 in Erlangen.

Course description

This course is devoted to phase-field fracture methods. Four different sessions 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 lecture notes are online at TIB with the DOI https://doi.org/10.15488/15172

Objectives and target groups

The target groups are doctoral researchers, Postdocs, and peers in Computational Mechanics and Applied Mathematics.

  • Modeling
  • Discretizations
  • Solvers
  • Adaptivity
  • Optimization
  • Simulations
  • Current developments

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.

Bio-sketch

Thomas Wick is a University Professor for Scientific Computing and the Managing Director of the Institute of Applied Mathematics (IfAM) at the Leibniz Universität Hannover (LUH) in Germany and he is a collaborator (chercheur visiteur) at Paris-Saclay University, ENS, France, at LMPS - Laboratoire de Mecanique Paris-Saclay.

He is a member of various national and international collaboration networks such as the Cluster of Excellence PhoenixD, the international research training group IRTG 2657 Computational Mechanics Techniques in High Dimensions (CoMeTeNd) as well as the South America Competence Center of Scientific Computing (SaCCC). His research interests are design, (open-access) implementation and analysis of numerical algorithms and space-time methods for nonstationary, nonlinear, coupled PDE systems and variational inequalities within the fields for computational fluid dynamics, solid mechanics, fluid-structure interaction, thermoporoelasticity, and crack propagation problems in elasticity and poroelasticity.

Therein, he is specifically interested nonlinear solvers, linear solvers, a posteriori error estimation, adaptive methods such as local mesh adaptivity with a particular emphasis on goal-oriented techniques using adjoints, and parallel high performance computing. These concepts are furthermore employed in numerical optimization for optimal control, optimal design and parameter estimation.

Thomas Wick published three books, one being translated into Chinese, co-edited one book and published over 120 peer-reviewed journal articles. Several publications are accompanied with open-source codes and research software developments. He has delivered more than 190 presentations at conferences and workshops, and he has taught more than 50 classes in eight countries.