A Modified Multilevel Scheme for Internal and External Constraints in Virtual Environments

Multigrid algorithms are gaining popularity in virtual reality simulations as they have a theoretically optimal performance that scales linearly with the number of degrees of freedom of the simulation system. We propose a multilevel approach that combines the efficiency of the multigrid algorithms with the ability to resolve multi-body constraints during interactive simulations. First, we develop a single level modified block Gauss-Seidel (MBGS) smoother that can incorporate constraints. This is subsequently incorporated in a standard multigrid V-cycle with corrections for constraints to form the modified multigrid V-cycle (MMgV). Numerical results show that the solver can resolve constraints while achieving the theoretical performance of multigrid schemes.