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On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations
Author(s) -
BrewittTaylor C. R.,
Johns P. B.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150103
Subject(s) - transmission line , field (mathematics) , space (punctuation) , line (geometry) , network model , electric power transmission , computer science , transmission (telecommunications) , maxwell's equations , mathematics , mathematical analysis , topology (electrical circuits) , geometry , engineering , telecommunications , combinatorics , database , pure mathematics , electrical engineering , operating system
It is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission‐line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission‐line network models used in the steady‐state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two‐dimensional example.