Modeling interaction between deformable and rigid objects efficiently and accurately is one of the most important tasks for interactive surgical simulation. The Finite Element Method (FEM) has become very popular in this context due to its versatility in representing elastic bodies with irregular geometric features and diverse material properties. In this work we propose a hybrid FEM approach to simulating realistic tissue behavior that uses a non-linear formulation in the vicinity of the interaction while employing a less accurate and inexpensive linear formulation elsewhere. A semi-implicit time stepping is used for the non-linear portion of the domain. This avoids expensive domain decomposition strategies required to maintain consistency at the interface and allows for regular system assembly using a non-overlapping interface and single solver for both domains. This study demonstrates the advantages of our novel approach, especially for the case of real-time surgical simulation.
Keywords: domain decomposition; finite element method; medical simulation.