An efficient integration technique for the voxel-based finite cell method

The finite cell method is a fictitious domain approach based on hierarchical Ansatz spaces of higher order. The method avoids time-consuming and often error-prone mesh-generation and favorably exploits Cartesian grids to embed structures of complex geometry in a simple-shaped computational domain thus shifting parts of the computational effort from mesh generation to the computation within the embedding finite cells of regular shape. This paper presents an effective integration approach for voxel-based models of linear elasticity that drastically reduces the computational effort on cell level. The applied strategy allows the pre-computation of an essential part of the cell matrices and vectors of higher order, representing stiffness and load, respectively. Several benchmark problems show the potential of the proposed method in particular for heterogeneous material properties as common in biomedical applications based on computer tomography scans. The applied strategy ensures a fast computation for time-critical simulations and even allows user-interactive simulations for models of moderate size at a high level of accuracy.