TLM for diffusion: the artefact of the standard initial conditions and its elimination within an abstract TLM suite
✍ Scribed by Peter Enders; Donard de Cogan
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 125 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0894-3370
- DOI
- 10.1002/jnm.400
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✦ Synopsis
Abstract
We demonstrate both analytically and numerically, that for the TLM algorithm for numerically solving the diffusion equation the standard initial conditions for the incident voltage pulses in terms of the initial concentration (or temperature) distribution introduce a significant numerical error. We discover the origin of this error and present an alternative prescription for computing the node voltages at the first time step which removes this artefact and exhibits distinctly improved numerical accuracy. For this, we introduce the term abstract TLM suite (ATS). An ATS is a numerical scheme which formally parallels a TLM scheme, but the scattering coefficients, ρ and τ, may assume values outside the interval [−1, 1] or may not correspond to the values of a real TLM network. Copyright © 2001 John Wiley & Sons, Ltd.