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Research Seminar: Complexity reduction in multiscale computational modelling, and CutFEM: a new generation of mesh independent finite element methods for multi-physics problems

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Speaker: Dr. Susanne Claus and Dr. Pierre Kerfriden (Cardiff University)
Event date: Tuesday, 24 October 2017 05:00 pm - 06:00 pm
Place: Room 3.350, Maison du Savoir
2, avenue de l'Université
L-4365 Esch-sur-Alzette

These two 30-minute talks are organised by the Mathematics Research Unit, in collaboration with SnT and the Luxembourg Mathematical Society.

Complexity reduction in multiscale computational modelling, with Dr. Pierre Kerfriden

In many modern engineering systems, such as micro-engineered composite structures or large-scale systems tailored for high-frequency dynamics, analysts need to predict physical phenomena over multiple scales. With ever increasing computational capabilities, high fidelity numerical simulations are increasingly considered as a reliable way to obtain such predictions. However, the numerical cost associated with high fidelity simulations over multiple scales remains tremendous for anything but academic test cases. In this presentation, I will discuss a series of recent developments at Cardiff University in the area of automatised model reduction algorithms that give analysts control over the computational cost. In this suite of algorithms, physical features that do not contribute to engineering outputs of interests are automatically identified and removed from the computational model, thereby reducing the numerical cost by several orders of magnitude. I will present examples of applications in several areas of computational engineering, namely electrostatics, linear vibrations and nonlinear fracture mechanics and explain how such approaches may help increase the performance and reliability of modern multilevel engineering systems.

CutFEM: a new generation of mesh independent finite element methods for multi-physics problems, with Dr. Susanne Claus

Traditional finite element methods rely on the discretisation of geometries with high quality meshes. However, for very complex problems such as engineering assemblies of interacting solids or unsteady multi-phase fluid flows, the construction of these high quality meshes can be prohibitively expensive and cumbersome. In this presentation, I will introduce a new cut finite element method which avoids meshing and instead uses a functional description of geometries. Such a description allows us to embed complex geometries in fixed, regular background grids with ease. I will show how a-priori finite element analysis can be used to develop cut finite element schemes (CutFEM) that are both accurate and stable. I will then present high-performance CutFEM algorithms for a range of complex multi-material problems such as unilateral contact between solids, fluid flows and laser ablation.

Susanne Claus is a research fellow at Cardiff School of Engineering, Cardiff University, since 2015. After finishing her PhD at Cardiff School of Mathematics in the field of computational rheology, she worked as a postdoctoral research at the University of Sussex (2012) and University College London (2013-2015). Her research focuses on the development of stabilised cut finite element methods for multi-physics problems. In particular, she is developing high performance finite element solutions for moving interface problems in Newtonian/non-Newtonian fluid mechanics as well as solid mechanics.

Pierre Kerfriden is a Senior Lecturer at Cardiff University, School of Engineering. His research interests focus on advanced methods in computational mechanics, in particular high-performance computing, optimisation, error control and adaptivitiy, inverse problems and data-assimilation, multiscale modelling, composite materials, nonlinear fracture mechanics, structural vibrations. He received the Outstanding Paper Award of the Literati Network and was nominated at the Rising Star awards; two of his 19 PhD students received the Best PhD Thesis prize of the UK Association for Computational Mechanics in Engineering.