Integration of a Multigrid ODE Solver into an Open Medical Simulation Framework

In this paper, we present the implementation of a Multigrid ODE solver in SOFA framework. By combining the stability advantage of coarse meshes and the transient detail preserving virtue of fine meshes, Multigrid ODE solver computes more efficiently than classic ODE solvers based on a single level discretization. With the ever wider adoption of the SOFA framework in many surgical simulation projects, introducing this Multigrid ODE solver into SOFA's pool of ODE solvers shall benefit the entire community. This contribution potentially has broad ramifications in the surgical simulation research community, given that in a single-resolution system, a constitutively realistic interactive tissue response, which presupposes large elements, is in direct conflict with the need to represent clinically relevant critical tissues in the simulation, which are typically be comprised of small elements.