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Heterogeneous Coupling for Implicitly Described Domains

Domain Decomposition Methods in Science and Engineering XXI, Volume 98, page 809--817 - 2014
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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.

Références BibTex

@InProceedings{EW14,
  author       = {Engwer, C. and Westerheide, S.},
  title        = {Heterogeneous Coupling for Implicitly Described Domains},
  booktitle    = {Domain Decomposition Methods in Science and Engineering XXI},
  series       = {Lecture Notes in Computational Science and Engineering},
  volume       = {98},
  pages        = {809--817},
  year         = {2014},
  editor       = {Erhel, Jocelyne and Gander, Martin J. and Halpern, Laurence and Pichot, Geraldine and Sassi, Taoufik and Widlund, Olof},
  publisher    = {Springer International Publishing},
  keywords     = {bulk-surface parabolic equations, unfitted discontinuous galerkin, surface finite elements, implicit surfaces, level set methods, reaction-diffusion},
  issn         = {978-3-319-05789-7},
  doi          = {10.1007/978-3-319-05789-7_78},
  url          = \{/2014/EW14},
}

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