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- Title:
On the convergence of the classical symmetrical condensed node-TLM scheme
- Document type:
- Zeitschriftenaufsatz
- Author(s):
- Rebel, J. N.; Aidam, M.; Russer, P.
- Abstract:
- This paper presents a proof of convergence of the transmission-line matrix (TLM) method with a symmetrical condensed node (SCN) in the classical formulation of Johns (1987). It is shown that the convergence order of the SCN-TLM method cannot simply be derived from observing the dispersion characteristics of the TLM mesh. The mapping between the discretized electromagnetic field and TLM wave amplitudes plays a decisive role. Although second-order convergence is observed for coarse discretizations, which are usually used in practice due to the limitations of memory resources, it is shown and numerically verified that the asymptotic convergence reduces to order 𝒪 (√Δt). Only using a bijective field mapping defined at the cell boundaries yields second-order convergence
- Keywords:
- electromagnetic field theory, transmission line matrix methods, boundary-value problems, electromagnetic wave propagation, finite difference methods, numerical stability, convergence of numerical methods, second-order convergence, transmission-line matrix method, asymptotic convergence, bijective field mapping, classical formulation, convergence order, discretized EM field, SCN-TLM method, symmetrical condensed node-TLM scheme, TLM wave amplitudes
- Journal title:
- Microwave Theory and Techniques, IEEE Transactions on
- Year:
- 2001
- Journal volume:
- 49
- Journal issue:
- 5
- Pages contribution:
- 954--963
- Fulltext / DOI:
- doi:10.1109/EUMA.2002.339423
- Print-ISSN:
- 0018-9480
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