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Discretization effects in TLM diffusion models. (English) Zbl 0957.78025

Summary: 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.

MSC:

78M25 Numerical methods in optics (MSC2010)
78A25 Electromagnetic theory (general)
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