Efficient effective-energy method for lattice-Greens-function simulations of fracture

This paper discusses a method for finding equilibria within the lattice-Greens-function formulation. The method involves the creation of an energy functional expressed just in terms of a small subset of the (>106) total number of degrees of freedom. It is much more efficient and robust numerically than former methods of solution of the Greens-function equations, particularly when the subset becomes scrO(103). The energy functional may be used in conjuction with state of the art conjugate gradient, quasi-Newton or simulated annealing methods to find minimum-energy configurations and compare their energies. In addition, if constraints are placed on the allowed relations between a few of the degrees of freedom then the method may be used to find the energies of unstable equilibria and hence activation energies.