Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/62431
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Type: Journal article
Title: Eigenvalue analysis and longtime stability of resonant structures for the meshless radial point interpolation method in time domain
Author: Kaufmann, T.
Engstrom, C.
Fumeaux, C.
Vahldieck, R.
Citation: IEEE Transactions on Microwave Theory and Techniques, 2010; 58(12):3399-3408
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2010
ISSN: 0018-9480
1557-9670
Statement of
Responsibility: 
Thomas Kaufmann, Christian Engström, Christophe Fumeaux and Rüdiger Vahldieck
Abstract: A meshless collocation method based on radial basis function (RBF) interpolation is presented for the numerical solution of Maxwell’s equations. RBFs have attractive properties such as theoretical exponential convergence for increasingly dense node distributions. Although the primary interest resides in the time domain, an eigenvalue solver is used in this paper to investigate convergence properties of the RBF interpolation method. The eigenvalue distribution is calculated and its implications for longtime stability in time-domain simulations are established. It is found that eigenvalues with small, but nonzero, real parts are related to the instabilities observed in time-domain simulations after a large number of time steps. Investigations showthat by using global basis functions, this problem can be avoided. More generally, the connection between the high matrix condition number, accuracy, and the magnitude of nonzero real parts is established.
Keywords: Eigenfunctions and eigenvalues
finite-difference methods
meshless methods
resonance
time-domain modeling
Rights: © 2010 IEEE
DOI: 10.1109/TMTT.2010.2081250
Published version: http://dx.doi.org/10.1109/tmtt.2010.2081250
Appears in Collections:Aurora harvest
Electrical and Electronic Engineering publications

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