Heterogeneous coupling for implicitly described domains. (English) Zbl 1382.65313
Erhel, Jocelyne (ed.) et al., Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Cham: Springer (ISBN 978-3-319-05788-0/hbk; 978-3-319-35548-1/pbk; 978-3-319-05789-7/ebook). Lecture Notes in Computational Science and Engineering 98, 809-817 (2014).
Summary: Modern imaging techniques yield high quality information of complex shaped microscopic structures. The unfitted discontinuous Galerkin method (UDG) offers an approach to solve partial differential equations 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.
For the entire collection see [Zbl 1381.65002].
For the entire collection see [Zbl 1381.65002].
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
numerical example; complex shaped microscopic structures; unfitted discontinuous Galerkin method; micro-CT imaging; domain decompositionReferences:
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