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Susanne Claus: Stabilised cut finite element methods for problems involving three or more materials in complex geometries

Tid: To 2017-11-30 kl 14.15 - 15.00

Plats: Room F11, Lindstedtsvägen 22, våningsplan 2, F-huset, KTH Campus.

Medverkande: Susanne Claus, Cardiff University

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Abstract:

In this presentation, we will introduce cut finite element schemes for problems with multiple materials. In the cut finite element method (CutFEM), PDEs are discretised on a regular background grid while the geometry of the problem is described independent of this background mesh. In our approach, we represent the geometry using multiple level set functions whose zero level sets describe interface and boundary locations. This means that interfaces and boundaries can intersect background mesh elements in an arbitrary manner. This yields two major challenges: (i) if an interface intersects a background element near element nodes ill-conditioning of the system matrices may occur; and (ii) to represent jumps and kinks in the solution inside elements these elements need to be enriched. This need for enrichments and for regularisation in the interface zones becomes particularly acute if three or more materials form triple or multiple junctions inside elements. In this presentation, we will show how we address these challenges and we will demonstrate the capability of our method in the context of contact problems between multiple materials.