Embedded Multigrid Approach for Real-Time Volumetric Deformation

Finding efficient and physically based methods to interactively simulate deformable objects is a challenging issue. The most promising methods addressing this issue are based on finite elements and multigrid solvers. However, these multigrid methods still suffer, when used to simulate large deformations, from two pitfalls, depending on the kind of grids hierarchy used. If embedded grids are used, approximating complex geometries becomes difficult, whereas when unstructured grids hierarchy is used, solving speed-up is reduced by the necessity to update coarser levels stiffness matrices. We propose a framework that combines embedded grids solving with fast remeshing. We introduce a new hierarchical mesh generator which can build a hierarchy of topologically embedded grids approximating a complex geometry. We also show how to take advantage of the knowledge of the stiffness matrix sparsity pattern to efficiently update coarse matrices. These methods are tested on interactive simulation of deformable solids undergoing large deformations.