A DOMAIN DECOMPOSITION METHOD FOR SOLVING THREE-DIMENSIONAL HEAT TRANSPORT EQUATIONS IN A DOUBLE-LAYERED THIN FILM WITH MICROSCALE THICKNESS

Abstract

We develop a finite difference method of the Crank?Nicholson type for solving three-dimensional heat transport equations in a double-layered thin film with microscale thickness. The three-dimensional implicit scheme is solved by using a preconditioned Richardson iteration, so that only two tridiagonal linear systems with unknowns at the interface are solved at each iteration. We then apply a parallel Gaussian elimination to solve these two tridiagonal linear systems and develop a domain decomposition algorithm for thermal analysis of the double-layered thin film. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained.