Exact stability conditions in upwinding‐scheme FDTD for the Boltzman transport equation. (15th August 2013)

• Record Type: Journal Article
• Authors: Chamanara, Nima; Caloz, Christophe
• Is Part Of: International journal of numerical modelling. Volume 27:Number 2(2014:Mar./Apr.)
• Page Start: 238
• Page End: 258
• Publication Date: 2013-08-15
• Subjects: Electric networks -- Mathematical models -- Periodicals; Electronics -- Mathematical models -- Periodicals; 621.3011
• DOI: 10.1002/jnm.1918
• Languages: English
• ISSNs: 0894-3370

Abstract

<abstract abstract-type="main" id="jnm1918-abs-0001"> <title>SUMMARY</title> <p id="jnm1918-para-0003">An in‐depth stability analysis of the FDTD method under the upwinding scheme for the Boltzmann transport equation (BTE) under the relaxation time approximation is provided. Both time forward and time backward difference equations are considered. In the time forward differencing case, a sufficient stability condition is derived for the BTE with variable coefficients, and a necessary and sufficient condition is derived for the BTE with constant coefficients. In the time backward differencing case, it is shown that the differencing equations are unconditionally stable. It is shown numerically that the previously reported stability conditions in the literature are not accurate. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>