| Time: |
January 20, 2015 |
| Lecturer: |
Dr. Andre Massing
Simula Research Laboratory, Center for Biomedical Computing, Oslo, Norway |
| Venue: |
Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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| Download as iCal: |
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Multi-domain and multi-physics problems with interfaces and parameter studies with changing geometricdomains can be severely limited by the use of conforming meshes when complex geometries in threespatial dimensions are involved.For instance, the simulation of blood flow dynamics in vessel geometries requires a series of highlynon-trivial steps to generate a high quality, full 3D finite element mesh from biomedical image data.Similar challenging and computationally costly preprocessing steps are required to transform geologicalimage data into conforming domain discretizations which respect complex structures such as faults andlarge scale networks of fractures. Even if an initial mesh is provided, the geometry of the model domainmight change substantially in the course of the simulation, as in e.g. fluid-structure interaction and freesurface flow problems, rendering even recent algorithms for moving meshes infeasible. Similar challengesarise in more elaborated optimization problems, e.g. when the shape of the problem domain is subject tothe optimization process and the optimization procedure must solve a series of forward problems fordifferent geometric configuration.In this talk, we focus on recent finite element methods on cut meshes (CutFEM) as one possible remedy.CutFEM technologies allow flexible representations of complex or rapidly changing geometries bydecomposing the computational domain into several, possibly overlapping domains. Alternatively,complex geometries only described by some surface representation can easily be embedded into astructured background mesh.In the first part of this talk, we briefly review how finite element schemes on cut and composite meshescan be designed by using Nitsche-type imposition of interface and boundary conditions. To make theformulations robust, optimally convergent and to avoid ill-conditioned linear algebra systems, so-calledghost-penalties are added in the vicinity of the boundary and interface. Finally, we demonstrate howCutFEM techniques can be employed to address various challenges from mesh generation tofluid-structure interaction problems, solving PDE on surfaces and optimization tasks.
