In the present work, we propose a new approach, the so-called compressed adaptive integration scheme (C-AIS), for the computation of the stiffness and mass matrices in fictitious domain methods requiring the integration of discontinuous functions. The novel approach extends the conventional quadtree-decomposition-based adaptive integration scheme (AIS) by an additional step, in which established image-compression techniques are exploited to decrease the number of integration sub-cells. The benefits of the C-AIS are manifold: First, the compression of the sub-cells inevitably leads to significant savings in terms of computational time required by the numerical integration. Second, the compression procedure, which is executed directly after the quadtree-decomposition algorithm, can be easily included in existing codes. Third, if applied to polynomial integrands, the C-AIS yields exactly the same accuracy as the conventional AIS. Finally, the fourth advantage is seen in the fact that the C-AIS can readily be combined with other approaches seeking a reduction of the number of integration points such as the Boolean-FCM. The efficiency of the C-AIS approach is presented in the context of the FCM based on Cartesian meshes applied to problems of linear elastostatics and modal analysis, while it is also suitable for the quadrature in other fictitious domain approaches, e.g., CutFEM and cgFEM.

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The acoustic behavior of a combustion engine is primarily dominated by the sound radiation of the oil pan. Therefore, the vibration behavior of the oil pan as the prominent noise emission source is investigated in this paper. The aim of this study is to present a new vibration reduction concept, which is based on the property of high damping possessed by granular materials. The efficiency of this concept is proven by measurements via a scanning laser vibrometer. Finally, it is shown that it is possible to create a lighter oil pan which shows much lower vibration amplitudes than the original one.