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Eigenvalue analysis and longtime stability of resonant structures for the meshless radial point interpolation method in time domain

Kaufmann, Thomas ; Engstrom, Christian LU ; Fumeaux, Christophe and Vahldieck, Rdiger (2010) In IEEE Transactions on Microwave Theory and Techniques 58(12 PART 1). p.3399-3408
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.... (More)

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 show that 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.

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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Eigenfunctions and eigenvalues, finite-difference methods, meshless methods, resonance, time-domain modeling
in
IEEE Transactions on Microwave Theory and Techniques
volume
58
issue
12 PART 1
article number
5597961
pages
10 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:78650265475
ISSN
0018-9480
DOI
10.1109/TMTT.2010.2081250
language
English
LU publication?
no
id
e08f2b97-14e9-428d-b7f2-467130ec911e
date added to LUP
2023-03-24 11:15:25
date last changed
2023-03-24 15:17:01
@article{e08f2b97-14e9-428d-b7f2-467130ec911e,
  abstract     = {{<p>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 show that 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.</p>}},
  author       = {{Kaufmann, Thomas and Engstrom, Christian and Fumeaux, Christophe and Vahldieck, Rdiger}},
  issn         = {{0018-9480}},
  keywords     = {{Eigenfunctions and eigenvalues; finite-difference methods; meshless methods; resonance; time-domain modeling}},
  language     = {{eng}},
  number       = {{12 PART 1}},
  pages        = {{3399--3408}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Microwave Theory and Techniques}},
  title        = {{Eigenvalue analysis and longtime stability of resonant structures for the meshless radial point interpolation method in time domain}},
  url          = {{http://dx.doi.org/10.1109/TMTT.2010.2081250}},
  doi          = {{10.1109/TMTT.2010.2081250}},
  volume       = {{58}},
  year         = {{2010}},
}