Alternating block Crank-Nicolson method for the 3-D heat equation
type: Item
instance of: scholarly article
title: Alternating block Crank-Nicolson method for the 3-D heat equation
zbMATH Open document ID: 0821.65060
DOI: 10.1016/0096-3003(94)90157-0
author: Jing Chen
published in: Applied Mathematics and Computation
publication date: 1995-05-11T00:00:00Z
review text: Recently, there has been growing interest in the parallel implementation of implicit methods. The alternating segment Crak-Nicolson and the alternating band and block Crank-Nicolson methods have been developed for one- and two-dimensional diffusion equations, respectively. In this paper the author extends the alternating block technique to a 3-dimensional problem and proposes a new numerical scheme called alternating block Crank-Nicolson (ABkC-N) method for the 3-dimensional linear heat equation in the unit cube. The Crank-Nicolson (C-N) scheme is an implicit form and is difficult to arrange for computation in sequence or in parallel. Out of consideration for parallelism, stability and accuracy, the author constructs the ABkC-N method by dividing the net region into finite blocks on which the computations are independent from each other. The ABkC-N scheme is unconditionally stable and is suitable to an MIMD computer. The numerical experiments show that the scheme is a little more accurate than the C-N scheme itself.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 753926
zbMATH Keywords: parallel computation
zbMATH Keywords: implicit methods
zbMATH Keywords: alternating band and block Crank- Nicolson methods
zbMATH Keywords: heat equation
zbMATH Keywords: stability
zbMATH Keywords: numerical experiments
reviewed by: Song Jiang
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)90157-0
OpenAlex ID: W1995356791
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description: scientific article; zbMATH DE number 753926