In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobi methods with overrelaxation for symmetric convex linear complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data (SIMD) computation paradigm promoted by the Compute Unified Device Architecture (CUDA) library for graphical processing unit (GPU) programming. The framework is anticipated to become a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow.

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