School on Advanced Topics in Computational Mechanics

Computational phase-field modelling - Dr Kris van der Zee


Course description: Computational phase-field modelling is a thriving paradigm in computational mechanics. Phase-field modelling refers to the mathematical description of physical systems with different phases separated by an evolving diffuse interface. Prime examples include the interface evolution in a single material, such as crack propagation, as well as between two, or more, distinct states arising in mixtures and multi-phase systems, such as in binary alloys, two-phase flows, solidification, grain and crystal growth, and the growth of cancerous tumors.

Course objective: The objective of the short-course is to give an accessible introduction to computational phase-field modelling, focusing on the questions:

  • What are the phase-field models?

  • Why do they work, and how do you solve them?

  • Where do phase-field models come from, and how are they derived?

Course contents

  • Examples: Phase-field fracture, the Navier-Stokes-Cahn-Hilliard system, phase-field solidification, mechano-biological mixtures

  • Principles: Free-energy dissipation, phase separation, phase transition, coarsening

  • Computational methods: Energy-stable time-stepping algorithms

  • Foundations: Truesdell’s continuum theory of mixtures, Gurtin-Coleman-Noll phase-field theory


Dr Kris van der Zee is an Associate Professor in the School of Mathematical Sciences at the University of Nottingham. Previously he was an Assistant Professor at Eindhoven University of Technology, a Postdoctoral researcher at the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin, and a Cum Laude PhD Graduate in Aerospace Engineering at Delft University of Technology. His research specializes in computational mechanics of interfacial phenomena, the mathematics of finite element methods, and more recently, the development and analysis of deep-learning algorithms within scientific computation.
He held a UK Royal Society International Exchange Fellowship, he was awarded a “Veni” Early Career Grant by the Netherlands Organisation for Scientific Research, and he was awarded a UK Royal Society Newton International Fellowship. He is Associate Editor of the Journal Engineering with Computers.

A primer on cut finite element methods - Prof. Dr.-Ing. Dominik Schillinger


Within the last 15 years, cut finite element methods, also known as fictitious domain, embedded domain, finite cell, unfitted or immersed finite element methods, have evolved into a mature and powerful simulation tool that is widely applied across the fields of computational solid and fluid dynamics [1, 2]. Cut finite element methods eliminate the need for boundary conforming meshes that often require time-consuming and error-prone mesh generation procedures, and thus help enable a seamless integration of complex geometric models into finite element analysis. In addition, cut finite element methods naturally accommodate changes of the geometric domain during the solution process, as required for instance in topology optimization or fluid-structure interaction.

The key to their success has been the resolution of three major technical challenges related to using cut finite elements:

1. Numerical quadrature: how can cut elements be integrated accurately and efficiently?

2. Boundary conditions: how can constraints be imposed accurately and robustly at surfaces that cut through elements?

3. Robustness: how can accuracy and efficiency be guaranteed in general simulation scenarios?

In this class, I start with a motivation for the development of cut finite element schemes, including a brief historic overview, and introduce the nature of the underlying challenges in comparison to standard boundary-fitted schemes. I then explain the main ideas and methods to effectively resolve the challenges of quadrature, boundary constraint imposition and robustness. I close with demonstrating the advantages of cut finite elements in practical simulation scenarios, including patient-specific analysis in biomedicine, isogeometric shell analysis of trimmed free-form CAD surfaces, and examples from computational fluid dynamics and fluid-structure interaction


Prof Schillinger’s research interests are in computational mechanics, focusing on the modelling and finite element analysis of multiphysics and multiscale mechanical systems. In particular, he strives to develop novel geometry-through analysis tools that enable the seamless transfer of complex geometric models from computer-aided design and biomedical imaging into simulation results. Specific applications that drive his work include the computational design of aerodynamic structures (for example, turbine blades) and the integration of computer simulations in clinical practice, with the goal of enabling new patient-specific treatments (for example, for bone osteoporosis).

Dominik’s work has been distinguished with a number of high-level research awards, in particular the IACM John Argyris Award, the GAMM Richard-von-Mises Prize, the ICE Zienkiewicz Medal, the NSF CAREER Award, and the EMI Leonardo da Vinci Award.

Introduction to Optimisation Using Metaheuristics - Prof Ender Özcan


Metaheuristics represent a set of high-level approaches supporting the development of heuristic optimisation algorithms. They often provide high-quality (not necessarily optimal) solutions to computationally hard problems in a reasonable amount of time. Over the past few decades, many highly effective metaheuristics, working on a variety of domains, have been presented. This seminar will be covering the fundamentals of metaheuristics focusing on combinatorial optimisation with case studies, including search paradigms, heuristic/operator types, classification of metaheuristics, algorithmic design issues, parameter tuning versus control, and more.


Ender Özcan is a Professor of Computer Science and Operational Research with the Computational Optimisation and Learning (COL) Lab at the University of Nottingham. His research lies at the interface of Computer Science, Artificial Intelligence and Operational Research. With over 150 refereed publications, he is one of the leading scientists in intelligent decision support, underpinned by advanced (hyper-/meta)heuristic optimisation techniques. He contributed and has been contributing to externally funded projects as principal investigator and co-investigator, supported by various funding bodies ranging from European Commission to Innovate UK. He is a co-founder and co-chair of the EURO Working Group on Data Science Meets Optimisation. He is a Senior Member of IEEE, an elected member of the EPSRC, and College Research Foundation - Flanders (FWO) Peer Review College. He is Associate Editor of the Journal of Scheduling and International Journal of Applied Metaheuristic Computing, and on the Editorial (Advisory) Board of the Engineering Applications of Artificial Intelligence Journal and International Journal of Intelligent Computing and Cybernetics.