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Exact stability conditions in upwinding‐scheme FDTD for the Boltzman transport equation
Author(s) -
Chamanara Nima,
Caloz Christophe
Publication year - 2013
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1918
Subject(s) - upwind scheme , stability (learning theory) , mathematics , boltzmann equation , constant (computer programming) , mathematical analysis , relaxation (psychology) , courant–friedrichs–lewy condition , convection–diffusion equation , variable (mathematics) , physics , computer science , discretization , thermodynamics , psychology , social psychology , machine learning , programming language
SUMMARY 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 & Sons, Ltd.