Use of a dynamic network for the TLM solution of diffusion problems

There is a class of material processing simulators which require solution o f the diffusion equation over a surface which is evolving due to some physi cal or chemical process related to the concentration of the diffusing speci es. Because of its explicit and unconditionally stable nature, the transmis sion line matrix (TLM) method is well suited to efficiently solve the diffu sion equation in these instances. However, the methodology for using TLM on a dynamic problem space is not well established. This paper describes the development of algorithms to handle the insertion, deletion and motion of TLM nodes along the one-dimensional surface of a tw o-dimensional thin film process simulator called GROFILMS. These routines a re completely compatible with concurrent time scaling to increase computati onal efficiency. Central to this development is the use of an asymmetric TL M cell which provides more flexibility for representation and minimizes the disturbance effects of these nodal operations. The scaling routines apply conservation of charge and continuity of current into the affected region t o recompute the scattered or the incident pulses as a result of the evolvin g network. Verification of these results through comparison with known anal ytic solutions is achieved where possible. (C) 1998 John Wiley & Sons, Ltd.