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Finite deffernce time‐domain approximation of Maxwell's equations with non‐orthogonal condensed TLM mesh
Author(s) -
Hein Steffen
Publication year - 1994
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1660070305
Subject(s) - mathematics , discretization , block matrix , maxwell's equations , matrix (chemical analysis) , generalization , finite element method , mathematical analysis , domain (mathematical analysis) , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , thermodynamics
A convex hexahedral TLM mesh of arbitrary shape is presented and the transmission‐line matrix method extended to any non‐orthogonal configuration. The novel mesh constitutes a natural generalization of Johns' condensed node. The associated TLM process is analysed and reconstructed as a genuine finite difference time‐domain algorithm. Nodal S‐parameters are derived from discretized Maxwell's equations and canonical stability criteria yield the TLM timestep. Unitarity is discussed and energy conservation confirmed in the non‐conductive case. A given block‐diagonal representation of the S‐matrix restrains processing time per node and iteration within the range of traditional methods. The shortcomings of the rigid classical grid, as the need for inaccurate staircasing approximations, are, however, ruled out. Our analysis takes advantage of the recently developed propagator integral approach.