Seminar Fictitious Domain and Immersed Boundary methods - Winter 16

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Term
Winter 2016/17
Lecturer
Dipl.-Math. Benjamin Uekermann, Stefan Gavranovic
Time and Place
see below for detailed schedule
Audience
Computational Science and Engineering (Seminar, module IN2183),
Informatics (Master-Seminar, module IN2107)
Tutorials
-
Exam
-
Semesterwochenstunden / ECTS Credits
2 SWS (2S) / 4 ECTS (TUM participants)
TUMonline
TUM Online




News & Dates

  • Kick-off: Thursday, October 27 at 09:00am in room MI 02.07.023
  • The distribution of the seminar topics is available at the Moodle page of the course
  • pre-course meeting: Friday June 24, 2:45pm, room: 00.08.036
  • Slides of the pre-course meeting are available for download


Description

Fictitious domain and immersed boundary methods have gained large interest over the last years, especially in the computational mechanics and computational fluid dynamics (CFD) research community. In these methods is the (finite element) discretization independent of the shape of the physical domain. This does not only prevent the critical process of mesh generation for complex domains, but it also offers the freedom of choice for structured, Cartesian or other discretization meshes. Therefore, it is especially important in the field of CFD and fluid structure interaction (FSI) where remeshing or moving mesh methods can have more computational cost. Another important application area is structural mechanics in biomedicine where models are obtained from voxelized sets of MRI images. The effort of mesh generation is replaced by a more advanced element integration which is an ongoing research effort together with the accurate imposition of boundary conditions. In this seminar, we will cover the different ingredients of fictitious domain and immersed boundary methods, discuss the current state of research and compare real world applications.


Topics

  • The Finite Cell Method (FCM)
  • The Tetrahedral Finite Cell Method (TetFCM)
  • Immersed Boundary methods for (linear) elasticity
  • Immersed Boundary methods for CFD
  • Generation of adaptive tetrahedral meshes
  • Parallel linear and direct solvers
  • Parallel system assembly strategies
  • Parallelization on GPUS
  • Parallelization on Xeon Phi
  • Adaptive integration based on space-trees
  • Volume integration for exact NURBS surface boundaries
  • Volume integration for triangulated surface boundaries
  • Dirichlet boundary condition - Nitsche's method
  • Dirichlet boundary condition - Penalty method
  • Boundary conditions for CT and voxel-based simulations
  • Volume Visualization of Fictitious Domain Simulation Results


Requirements

For successful completion of the seminar course you have to fulfil the following tasks:

  • solid understanding of your topic (e.g. by implementation of the underlying algorithm)
  • writing of a paper (about 6 pages)
  • presentation (30 min + discussion)
  • participation in the presentations of all other participants
  • deadlines: t.b.a.

Literature

Introduction to the topic

  • D. Schillinger, M. Ruess: The Finite Cell Method: A review in the context of higher-order structural analysis of CAD and image-based geometric models. Archives of Computational Methods in Engineering, 22(3):391–455, 2015.
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