Title: New developments in integrators and soft tissue simulation tools for Simbios
In this talk I will present a novel method for the simulation of the mechanics of soft tissue based on a discontinuous Galerkin framework for nonlinear elasticity. Discontinuous Galerkin methods are based on using finite element spaces that fail to be continuous across element boundaries to approximate smooth solutions. This added degree of flexibility pays off by displaying outstanding behavior for near incompressible materials and a notoriously enhanced robustness in comparison with traditional finite elements for general nonlinear elasticity problems. I will discuss the formulation and its stability, and show the results of the numerical tests. On the second part of the talk I will introduce the recently created parallel asynchronous variational integrators, which extend the idea of using multiple time-steps in a simulation to work in a scalable way in parallel environments. Although we have only used these integrators for finite element discretizations, they could potentially be extended to molecular dynamics systems with short and long ranged forces.