Existing multigrid methods for cloth simulation are based on geometric multigrid. While good results have been reported, geometric methods are problematic for unstructured grids, widely varying material properties, and varying anisotropies, and they often have difficulty handling constraints arising from collisions. This paper applies the algebraic multigrid method known as smoothed aggregation to cloth simulation. This method is agnostic to the underlying tessellation, which can even vary over time, and it only requires the user to provide a fine-level mesh. To handle contact constraints efficiently, a prefiltered preconditioned conjugate gradient method is introduced. For highly efficient preconditioners, like the ones proposed here, prefiltering is essential, but, even for simple preconditioners, prefiltering provides significant benefits in the presence of many constraints. Numerical tests of the new approach on a range of examples confirm 6 − 8× speedups on a fully dressed character with 371k vertices, and even larger speedups on synthetic examples.
This paper presented a new preconditioner for linear systems formed in implicit cloth simulations by developing an algebraic multigrid hierarchy based on the underlying PDEs and discretization. The SA solver provides a faster solution than existing methods for typical problems with 25, 000 vertices or more. For problems that are stiffer, have smaller mass, or are subjected to larger time steps, the advantages of the method increase and show speedups for smaller problems as well.
To realize the full potential of the SA in cloth simulation and attain near optimal scaling in the presence of collisions, we had to pair it with our new PPCG method. SA+PPCG is attractive because no changes need to be made to existing collision