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.