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

This 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