Truncated Newton-Raphson Methods for Quasicontinuum Simulations

摘要

The quasicontinuum method provides an efficient way to simulate the mechanical response of relatively large crystalline materials at zero temperature by combining continuum and atomistic approaches. Unconstrained optimization constitutes the key computational kernel of this method. The efficiency of the techniques for minimization depends on both the time needed to evaluate the energy expression and the number of iterations needed to converge to the minimum. In this research, we report the effectiveness of the truncated Newton-Raphson method and quasi-Newton method with low-rank Hessian update strategy that are evaluated against the full Newton-Raphson and preconditioned nonlinear conjugate gradient implementation. Results of illustrative examples mainly focus on the number of minimization iterations to converge and CPU time for the two-dimensional nanoindentation and shearing grain boundary problems.