On the convergence of the transfinite‐element method
ISSN: 0332-1649
Article publication date: 19 June 2007
Abstract
Purpose
The convergence of the transfinite‐element (TFE) method for high frequency methods is analyzed in this paper. Two different potential formulations will be compared in the frequency and time domain.
Design/methodology/approach
The A*‐and A,v‐formulation for time domain and frequency domain transfinite elements are described. The convergence properties of the methods are investigated and demonstrated on a simple test problem.
Findings
It is shown that the convergence of the frequency domain method depends also on the discretization of areas where the field values do not change very much. A numerical example shows that for the calculation of the whole frequency range, the time domain approach is much more faster than the frequency domain method.
Research limitations/implications
Further, work should also cover additional formulations like, e.g. the T,Φ‐formulation.
Practical implications
Pros and cons of different formulations and methods for solving high frequency problems for printed circuit boards or microwave structures are investigated.
Originality/value
The originality of the paper is the comparison, the discussion and the explanations of the convergence of the TFE method for wave propagation.
Keywords
Citation
Weiß, B., Bíró, O., Caldera, P., Hollaus, K., Paoli, G., Preis, K. and Stockreiter, C. (2007), "On the convergence of the transfinite‐element method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 3, pp. 600-611. https://doi.org/10.1108/03321640710751082
Publisher
:Emerald Group Publishing Limited
Copyright © 2007, Emerald Group Publishing Limited