Jia-Ming Lu, Tailing Yuan, Zhe-Han Mo, Shi-Min Hu
This research presents an efficient multigrid solver for deformable body simulations on unstructured tetrahedral meshes. The method combines the Full Approximation Scheme with Galerkin formulation and introduces a matrix-free vertex block Jacobi smoother that eliminates the computational burden of dense coarse matrices. The approach supports both piecewise constant and linear Galerkin formulations and achieves up to 6.9x speedup over traditional methods. Comprehensive GPU optimization techniques address parallel architecture challenges through Morton sorting, grid reduction, and spatial hashing. Extensive experiments demonstrate robust convergence across varying mesh resolutions, material stiffness values, extreme deformations, and complex collision scenarios, enabling practical simulation of million-vertex meshes at interactive frame rates.