An important advantage of the proposed method is that it can be added in a modular fashion to already existing codes. This is realized by introducing an additional step, in which the local integration mesh is simplified using data compression techniques leading to fewer integration domains/points. In this contribution, the often used, robust octree-decomposition-based integration scheme is enhanced by a novel approach reducing the computational effort when evaluating the discontinuous integrals. For optimal convergence rates and the efficiency of the simulation in general, special integration schemes have to be used in such elements. Since the mesh does not conform to the geometry, cut elements arise that are intersected by domain boundaries. Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and accurate simulation of complex geometries by utilizing higher-order shape functions and an unfitted discretization based on rectangular elements.
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