Two-Level Finite Difference Methods for Simulating the High-Dimensional Lagging Models of Heat Conduction. (3rd July 2017)

• Record Type: Journal Article
• Authors: Deng, Dingwen; Jiang, Yaolin
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 7(2017)
• Page Start: 831
• Page End: 860
• Publication Date: 2017-07-03
• Subjects: ADI method -- convergence -- finite difference method -- heat transfer equation at microscale; 65M06 -- 65M12 -- 65M15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1287727
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Heat transfer at microscale plays an important role in microtechnology applications. First, this paper is concerned with the numerical solution of a two-dimensional (2D) heat transfer equation at microscale through a second-order alternating direction implicit (ADI) method. By the discrete energy method, it is shown that the ADI solution converges to the exact solution with a convergence order of in L 2 -norm. Second, the ADI method is generalized to numerically solve the three-dimensional (3D) problem, and provides numerical solutions of order two in both time and space. Finally, numerical results testify the temporal and spatial accuracy of the ADI method.