An adaptive hybrid time‐stepping scheme for highly non‐linear strongly coupled problems

Abstract

AbstractThis paper deals with the design and implementation of an adaptive hybrid scheme for the solution of highly non‐linear, strongly coupled problems. The term ‘hybrid’ refers to a composite time stepping scheme where a controller decides whether a monolithic scheme or a fractional step (splitting) scheme is appropriate for a given time step. The criteria are based on accuracy and efficiency. The key contribution of this paper is the development of a framework for incorporating error criteria for stepsize selection and a mechanism for choosing from splitting or monolithic possibilities. The resulting framework is applied to silylation, a highly non‐linear, strongly coupled problem of solvent diffusion and reaction in deforming polymers. Numerical examples show the efficacy of our new hybrid scheme on both two‐ and three‐dimensional silylation simulations in the context of microlithography. Copyright © 2005 John Wiley & Sons, Ltd.