Molecular dynamics integration with bonds constrained to equilibrium values is a common approach used to increase the feasible timestep and hence reduce the overall simulation time. Here we analyze the widely used numerical iterative scheme for constrained molecular dynamics simulations, SHAKE, in a general algorithmic framework, from which SHAKE's relationship to nonlinear solvers can be established. Using the nonlinear SOR-Newton iterative method, we define an accelerated variant of SHAKE, called SHAKE-SOR, and prove a fundamental relationship between SHAKE-SOR and SOR-Newton. Based on this relationship, the convergence of SHAKE-SOR is proved in the framework of nonlinear SOR theory. Numerical results show that SHAKE-SOR can significantly improve the performance of standard SHAKE by reducing the number of iterations per timestep through an optimal parameter choice.

Submitted to a special issue of Methods and Applications of Analysis dedicated to Prof. Cathleen Morawetz of the Courant Institute

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