Interactive Physically Based Simulation - Efficient Higher-Order Elements, Multigrid Approaches and Massively Parallel Data Structures

This thesis covers interactive physically based simulation for applications such as computer games or virtual environments. Interactivity, i.e., the option that a user can influence a system, imposes challenging requirements on the simulation algorithms. A simple way to achieve this goal is to drastically limit the resolution in order to guarantee this low computation time. However, with current methods the number of degrees of freedom will be rather low, which results in a low degree of realism. This is due to the fact that not every detail that is important for realistically representing the physical system can be resolved. This thesis contributes to interactive physically based simulation by developing novel methods and data structures. These can be associated with the three pillars of this thesis: more accurate discrete representations, efficient methods for linear systems, and data structures and methods for massively parallel computing. The novel approaches are evaluated in two application areas relevant in computer generated animation: simulation of dynamic volumetric deformation and fluid dynamics. The resulting accelerations allow for a higher degree of realism because the number of elements or the resolution can be significantly increased.