Past Event: Oden Institute Seminar

The Finite Cell Method: Some Principles and Recent Progress

Ernst Rank, Lehrstuhl für Computation in Engineering, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München

Abstract

The Finite Cell Method (FCM), a high order fictitious domain approach, can be connected in a very natural way to geometric modelling based on Space Partitioning Techniques or on Constructive Solid Geometry (CSG). It thus shares its central philosophy with Isogeometric Analysis, where the principles of Spline-based geometric modelling and finite element-like numerical approximations are united. In this lecture basic ideas of the FCM are summarized and recent extensions concerning optimal local refinement and transient geometries are presented. A re-interpretation of the fictitious domain in the sense of a ‘third material’ opens the way for a modified contact formulation without the necessity of contact search. Verification and validation of FCM is discussed for some biomechanical problems, where extensive comparison with experiments on human femurs have been conducted. Bio: Prof. Dr. Ernst Rank studied mathematics and physics at the Ludwig-Maximilians-Universität München. He obtained his doctoral degree from the Faculty for Civil Engineering and Geodesy of Technische Universität München (TUM) in 1985. After positions at the University of Maryland, College Park, USA and at the Corporate Research and Technology of SIEMENS AG he was appointed associate professor at the University of Dortmund in 1990. Since 1997 he holds the chair for Computation in Engineering of the Technische Universität München. From 2002 to 2008 he was First Vice President of TUM. Since 2006 he is Founding Director of the TUM International Graduate School of Science and Engineering. His research interests cover many aspects in Computational Engineering with contributions ranging from adaptive and high order finite elements to multi-physics or multi-scale problems, geometric modelling and Building Information Models.