Domain decomposition and heterogeneous modeling used in solving a moving boundary problem

Abstract

PurposeTo provide an excellent numerical method to simulate an important industrial process – wet chemical etching problem.Design/methodology/approachA mathematical model describing the wet chemical etching process is formulated in terms of a parabolic variational inequality and a non‐overlapping domain decomposition (DD) method is proposed in the etching region, where a partial differential equation is treated in one sub‐domain, while a variational inequality is considered in the second sub‐domain. A Robin boundary condition with a parameter whose optimal value is to be found is enforced on the common boundary between these two sub‐domains. Finite difference technique with projection and the Crank‐Nicholson scheme for the time discretization are the major numerical tools utilized in this paper.FindingsThe proposed numerical method has achieved the best numerical performance for the famous wet chemical etching process among all the numerical schemes applied to this problem. It also shows the great computational power of domain splitting technique.Research limitations/implicationsLack of parallel supercomputer system limits the authors to perform further numerical tests with extremely large data. This will be done in the future.Practical implicationsThis is a very useful paper for the academic researchers and industry engineers who wish to develop more advanced numerical methods to simulate various kinds of industry processes along the research direction from this paper.Originality/valueThis paper provides a new and promising version of DD method in the field of moving boundary problems and offers a practical way to simulate wet chemical etching process for the engineers and scientists in the related field.