Course Objectives.
Standard numerical methods like the FEM and FVM are widely established in today's engineering practice. They are well-suited for the approximation of smooth solutions. However, in the real world, there is an infinite number of examples where field quantities do not behave smoothly but show jumps, kinks, singularities, etc. For example in solids, stresses and strains are discontinuous along material interfaces and singular at crack tips. In fluids, pressure and density change rapidly near shocks and the velocity gradient can be extremely large in boundary layers. In contrast to standard numerical methods, the XFEM enables the approximation of non-smooth solutions with optimal accuracy.
This is achieved by a local enrichment of the approximation space such that the special solution properties are considered appropriately. The XFEM is in the focus of intensive research activities and is currently realised in commercial finite element software tools.
This seminar is designed for graduate and doctoral students as well as developers from industry with interest in the XFEM and its wide applications.
Time Schedule.
July 5-7 2013, 20 units of instruction,
Friday and Saturday: 8:30-10:00, 10:30-12:00, 13:30-15:00, 15:30-17:00 and
Sunday: 8:30-10:00, 10:30-12.00, 13:30-15:00.
  • Basics of XFEM I: weighted residuals, enriched approximation
  • Basics of XFEM II: properties of enriched approximations
  • Implementation of XFEM: numerical integration, assembly, post-processing
  • Tutorial A: implementation in MATLAB, 1-D: diffusion problem
  • XFEM in structural mechanics I: bi-material problems, corrected XFEM
  • XFEM in structural mechanics II: cracks and crack growth
  • XFEM in structural mechanics III: finite deformation, non-linear materials
  • Tutorial B: implementation in MATLAB, 2-D: inclusions and cracks
  • XFEM in fluid mechanics: transient problems, moving fronts, two-fluid flows
  • XFEM in multi-physics: fluid-structure interaction
  • Background of XFEM: partition-of-unity method, intrinsic XFEM
Requirements and Credits.
Attending lectures and successful completion of tutorial exercises will be credited with 3 ECTS.
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Course Material.
The course material will consist of copies of a comprehensive manuscript (lecture notes), survey papers by the lecturers, recent manuscripts and a literature overview. Moreover, the participant will have access to computer code with a MATLAB implementation of the XFEM and examples discussed in the tutorials and hands-on sections.
Thomas-Peter Fries studied at the Technical University of Braunschweig in Germany under supervision of Prof. Hermann G. Matthies. In his dissertation, he developed a coupled meshfree/meshbased method for complex fluid-structure interaction problems. Dr. Fries was a post-doctoral fellow at the Northwestern University in Chicago, USA, in the research group of Prof. Ted Belytschko. From 2006-2012, Dr. Fries was head of an independent junior research group with the title Numerical methods for discontinuities in continuum mechanics funded by the Emmy-Noether program of the German Research Association (DFG). After being in industry (division of Schlumberger) he was appointed Professor for Structural Analysis at the University of Graz (Austria) in 2013.
Andreas Zilian studied Civil Engineering at the Technische Universität Berlin from which he graduated in 2001. Awarded with a scholarship by the German Research Foundation (DFG), he joined the Graduate Doctoral School "Interaction of Structure and Fluid" at the Technische Universität in Braunschweig. After completion of his PhD in 2005, Dr. Zilian became invited post-doctoral researcher at the Conservatoire National des Art et Métiers (CNAM) in Paris. The development of enriched finite element technologies for the simulation of multi-physics problems and investigation of efficient discrete descriptions of evolving discontinuities in a level-set context together with the realisation of the XFEM-concept in the framework of space-time finite elements is one of his research focuses. In 2006 he was appointed Assistant Professor at the Institute for Structural Analysis at TU Braunschweig and became Executive Director and Dean of Studies of the international Master programme Computational Sciences in Engineering. Prof. Dr. Andreas Zilian holds the chair of Statics and Structural Analysis at the University of Luxembourg since September 2011.