Unconditionally Stable Finite Difference Scheme and
Iterative Solution of 2D Microscale Heat Transport Equation

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Jennifer J. Zhao
Department of Mathematics and Statistics
University of Michigan at Dearborn
Dearborn, MI 48128-1491, USA

Abstract

A two dimensional time dependent heat transport equation at the microscale is derived. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned Conjugate Gradient method. Numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure.


Key words: Heat transport equation, finite difference, preconditioned Conjugate Gradient, Crank-Nicholson integrator.

Mathematics Subject Classification: 65M06, 65N12.


Download the compressed postscript file micro2d.ps.gz, or the PDF file micro2d.pdf.
This paper has been published in Journal of Computational Physics, Vol. 170, pp. 261-275 (2001).

Also as Technical Report 303-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000.

This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences.