A multigrid framework for real-time simulation of deformable bodies

In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and non-linear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates.