Heterogeneous Coupling for Implicitly Described Domains

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 98)

Abstract

Modern imaging techniques yield high quality information of complex shaped microscopic structures. The Unfitted Discontinuous Galerkin method (UDG) offers an approach to solve PDEs on implicitly described domains, e.g. obtained using micro-CT imaging, without the need to construct a geometry-resolving mesh. The domain description uses a level set based formulation; still domain boundaries are incorporated explicitly. We present an extension of the UDG method to incorporate processes on manifolds in a heterogeneous domain-decomposition framework. Using an explicit reconstruction of the implicit domain boundary it is possible to couple level set based surface problems on the boundary with domain problems.

Notes

Acknowledgements

The authors thank Wolfgang Giese (HU Berlin) for providing the budding yeast model which is based on [12]. All implementations were done using the frameworks DUNE [4] and DUNE-UDG [8].

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute for Computational and Applied MathematicsUniversity of MuensterMuensterGermany

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