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  4. Cut Finite Element Methods for Interface Problems in Computational Mechanics

Nov

18

Friday

Cut Finite Element Methods for Interface Problems in Computational Mechanics

2.00pm

Seminars

Staff, Students, Academics

Speaker: Prof Erik Burman, Chair of Computational Mathematics, UCL

Research Centre: Turbulence and Flow Control Research Group

Title: Cut Finite Element Methods for Interface Problems in Computational Mechanics

Abstract:

An important problem in computational mechanics is the treatment of boundaries or interfaces in an efficient, robust and accurate manner. Particularly challenging are problems involving the coupling of physical systems with different characteristics over the interface and where the interface position is an unknown of the system. This kind of problem occurs in a variety of applications, for instance in air cooling of machine parts, fluid structure interaction or shape optimisation. The use of standard techniques for the computation of such problems easily leads to a situation with a considerable computational overhead caused by remeshing and interpolation between different computational meshes. In this talk we will advocate a different approach to interface problems where the interface is allowed to cut through computational cells and the effect of the interface is built into the approximation space and the variational formulation. For a review of recent developments in this direction see Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, André CutFEM: discretizing geometry and partial differential equations. Internat. J. Numer. Methods Engrg. 104 (2015), no. 7, 472–501.

The method draws from previous ideas from XFEM and discontinuous Galerkin methods. We will show in a model fictitious domain case how the method may be designed to preserve both the accuracy and the robustness of a standard “fitted” finite element method. Then we will consider a series of more advanced applications including fluid-structure interaction, shape optimisation and transport via the cell-membrane surface in which a bulk partial differential equation couples to a surface partial differential equation. The discussion will be illustrated by computational examples.

Short Bio:

Erik Burman is the Chair of Computational Mathematics at UCL since 2013. He defended his PhD thesis, “Adaptive finite element methods for compressible two-phase flows” at Chalmers University of Technology in 1998. Then spent two years as a post doc at Ecole Polytechnique working on adaptive methods in computational combustion. From 2000-2007 he was a research associate at the Ecole Polytechnique Federale de Lausanne working on finite element methods for solidification problems and cardio vascular flows. In 2007 he moved to Sussex University for a full professorship in Mathematics. His current research interests include unfitted finite element methods for multi-physics interface problems in computational mechanics, computational methods for high Reynolds flow and stabilised methods for inverse and ill-posed problems.

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When & where

2.00pmFriday 18th November 2016

ELG14 City, University of London Northampton Square London EC1V 0HB United Kingdom