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.
| Original language | English |
|---|---|
| Pages (from-to) | 261-275 |
| Number of pages | 15 |
| Journal | Journal of Computational Physics |
| Volume | 170 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jun 10 2001 |
Bibliographical note
Funding Information:1URL: http://www.cs.uky.edu/˜jzhang. The research of this author was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0043861, and in part by the University of Kentucky Center for Computational Sciences. 2URL: http://www.umd.umich.edu/˜xich.
Keywords
- Crank-Nicholson integrator
- Finite difference scheme
- Heat transport equation
- Preconditioned conjugate gradient
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics