Heterogeneous Coupling for Implicitly Described Domains

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.