Decomposing cloth

Implicit schemes have become the standard for integrating the equations of motion in cloth simulation. These schemes, however, require the solution of a system representing the entire, fully connected cloth mesh at each time step. In this paper we present techniques that dynamically improve the sparsity of the underlying system, ultimately allowing the mesh to be decomposed into multiple components which can then be solved more efficiently and in parallel. Our techniques include a novel adaptive implicit-explicit (IMEX) scheme which takes advantage of simulation parameters, locally in both space and time, to minimize the coupling of the system. This scheme further directly improves the efficiency of the computation at each time step. Other sparsity improvements are obtained by exploiting the physical model of Choi and Ko (2002), as well as static constraints in the system. In addition, we present a <i>modified</i> preconditioner for the modified preconditioned conjugate gradient (MPCG) technique of Baraff and Witkin (1998), improving its performance by taking constraints into account.

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