Iterative Solution and Finite Difference Approximations
to 3D 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


Numerical computation techniques are proposed to solve a three dimensional time dependent microscale heat transport equation. 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 resulting sparse linear system at each time step with a few iterative methods and their performances are compared experimentally. Numerical experiments are presented to demonstrate 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.

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This paper has been accepted for publication in Mathematics and Computers in Simulation. Technical Report 320-01, Department of Computer Science, University of Kentucky, Lexington, KY, 2001. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, and CCR-0043861.