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In my research, I am mainly focused on immersed boundary methods, such as the finite cell method (FCM), which enables an efficient and accurate simulation of geometrically complex problems by an unfitted geometry discretization and higher-order approximation spaces. I have developed various approaches for improved numerical computation of the discontinuous integrals arising in these methods, that can be deployed, e.g., for nonlinear analysis of 3D structures and multi-material problems. In the latter case, the integration scheme incorporates an appropriate local enrichment of the approximation space to handle immersed material interfaces. My recent research topic is concerned with efficient code verification techniques for immersed boundary simulations of linear, nonlinear, steady-state, and transient problems of structural mechanics.