On the convergence of the classical symmetrical condensed node-TLM scheme

Author

Rebel, Jürgen N. ; Aidam, Martin ; Russer, Peter

Author_Institution

Inst. fur Hochfrequenztechnik, Infineon Technol. AG, Munich, Germany

Volume

49

Issue

5

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

954

Lastpage

963

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

boundary-value problems; convergence of numerical methods; electromagnetic field theory; electromagnetic wave propagation; finite difference methods; numerical stability; transmission line matrix methods; SCN-TLM method; TLM wave amplitudes; asymptotic convergence; bijective field mapping; classical formulation; convergence order; discretized EM field; second-order convergence; symmetrical condensed node-TLM scheme; transmission-line matrix method; Convergence of numerical methods; EMP radiation effects; Electromagnetic fields; Electromagnetic propagation; Finite difference methods; Maxwell equations; Space stations; Symmetric matrices; Transmission line matrix methods; Transmission lines;

fLanguage

English

Journal_Title

Microwave Theory and Techniques, IEEE Transactions on

Publisher

ieee

ISSN

0018-9480

Type

jour

DOI

10.1109/22.920154

Filename

920154