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Discretization effects in TLM diffusion models
Author(s) -
Wilkinson A. J.,
Pulko S. H.,
Saidane A.
Publication year - 2000
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/(sici)1099-1204(200001/02)13:1<59::aid-jnm382>3.0.co;2-9
Subject(s) - discretization , impulse (physics) , mathematics , invariant (physics) , diffusion equation , convergence (economics) , diffusion , computer science , mathematical analysis , physics , economy , quantum mechanics , economic growth , economics , mathematical physics , thermodynamics , service (business)
The standard methods for bringing a TLM diffusion model to convergence are necessary but tedious. However, much time and effort can be saved if the initial choices of elemental size and iteration timestep are appropriate. Here we consider the general form of the solution to the diffusion equation and sample the component dynamics to determine the impulse invariant response. We then derive a convenient method for charting the discrepancy between the coefficients of the continuous description and the impulse invariant transformation, as this discrepancy varies with discretization of space and time. The use of the curves in estimating appropriate elemental size and iteration timestep is described. Copyright © 2000 John Wiley & Sons, Ltd.