MS17 - Immersed Boundary Methods for Problems in Linear and Nonlinear Statics and Dynamics

Keywords: Immersed boundary methods; Cut elements; Statbilization; Critical time step size; Quadrature rules; Mass lumping

Organizers:
Lars Radtke (1) – lars.radtke@tuhh.de
Tim Bürchner (2) – tim.buerchner@tum.de
Sascha Eisenträger (3) – sascha.eisentraeger@ovgu.de
Philipp Kopp (4) – philipp.kopp@uni-weimar.de

Affiliations:
(1) Numerical Structural Analysis with Application in Ship Technology, Institute for Ship Structural Design and Analysis (M-10), Hamburg University of Technology, Germany
(2) Chair of Computational Modeling and Simulation, Technical University of Munich, Germany
(3) Faculty of Mechanical Engineering, Institute of Mechanics (IFME), Otto von Guericke University Magdeburg, Germany
(4) Chair of Data Science in Civil Engineering, Bauhaus-Universität Weimar, Germany

Abstract:
Avoiding the need for mesh generation for problems with complex geometries, immersed boundary methods (IBM) are constantly gaining in popularity. Concrete methods include the finite cell method (FCM), the cut finite element method (cutFEM), and the Cartesian grid FEM (CgGEM). While these methods are already used in a wide range of applications, certain problem types need further developments targeting the efficiency and the stability of IBM. Regarding the efficiency, in particular a reduction of the number of quadrature points is of interest. This recently led, e.g, to the development of moment fitting methods. Regarding the stability, in particular nonlinear problems and dynamic problems solved with explicit time integration method pose challenges. Here, undesired large deformation in the fictitious domain and unfeasibly small critical time step sizes call for further developments.

To this minisymposium we invite researchers from all fields of engineering and mathematics that further develop and/or apply immersed boundary methods.