An Approach to Solving Multiparticle Diffusion Exhibiting Nonlinear Stiff Coupling

A methodology for handling a class of stiff multiparticle parabolic PDE's in one and two dimensions is presented. The particular example considered in this work is the interaction and diffusion of two point defects in silicon, interstitials and vacancies. Newton's method, latency techniques, and second-order time-stepping approaches all contribute in significantly reduced computation times. A general class of diffusion-reaction problems is defined and conditions under which the corresponding Newton matrix is invertible and Newton's method converges to a globally unique solution are derived. The convergence properties of the purely reactive system are also derived and compared to those given by a Picard iteration. Application of basic iterative matrix techniques for the general diffusion-reaction system is discussed and specific numerical examples of point defect kinetics are given.