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Recent developments of the meshless radial point interpolation method for time-domain electromagnetics

Kaufmann, Thomas ; Yu, Y. LU ; Engström, C. LU ; Chen, Z. LU and Fumeaux, C. (2012) In International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 25(5-6). p.468-489
Abstract

Meshless methods are a promising new field in computational electromagnetics. Instead of relying on an explicit mesh topology, a numerical solution is computed on an unstructured set of collocation nodes. This allows to model fine geometrical details with high accuracy and facilitates the adaptation of node distributions for optimization or refinement purposes. The radial point interpolation method (RPIM) is a meshless method based on radial basis functions. In this paper, the current state of the RPIM in electromagnetics is reviewed. The localized RPIM scheme is summarized, and the interpolation accuracy is discussed in dependence of important parameters. A time-domain implementation is presented, and important time iteration aspects... (More)

Meshless methods are a promising new field in computational electromagnetics. Instead of relying on an explicit mesh topology, a numerical solution is computed on an unstructured set of collocation nodes. This allows to model fine geometrical details with high accuracy and facilitates the adaptation of node distributions for optimization or refinement purposes. The radial point interpolation method (RPIM) is a meshless method based on radial basis functions. In this paper, the current state of the RPIM in electromagnetics is reviewed. The localized RPIM scheme is summarized, and the interpolation accuracy is discussed in dependence of important parameters. A time-domain implementation is presented, and important time iteration aspects are reviewed. New formulations for perfectly matched layers and waveguide ports are introduced. An unconditionally stable RPIM scheme is summarized, and its advantages for hybridization with the classical RPIM scheme are discussed in a practical example. The capabilities of an adaptive time-domain refinement strategy based on the experiences on a frequency-domain solver are discussed.

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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
adaptive refinement, collocation method, meshless methods, radial basis function, radial point interpolation method, time domain, unconditional stability
in
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
volume
25
issue
5-6
pages
22 pages
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:84862862274
ISSN
0894-3370
DOI
10.1002/jnm.1830
language
English
LU publication?
yes
id
c9314c53-4b95-4a82-973d-d5c1e53ab88b
date added to LUP
2023-03-24 11:11:36
date last changed
2023-04-28 10:51:15
@article{c9314c53-4b95-4a82-973d-d5c1e53ab88b,
  abstract     = {{<p>Meshless methods are a promising new field in computational electromagnetics. Instead of relying on an explicit mesh topology, a numerical solution is computed on an unstructured set of collocation nodes. This allows to model fine geometrical details with high accuracy and facilitates the adaptation of node distributions for optimization or refinement purposes. The radial point interpolation method (RPIM) is a meshless method based on radial basis functions. In this paper, the current state of the RPIM in electromagnetics is reviewed. The localized RPIM scheme is summarized, and the interpolation accuracy is discussed in dependence of important parameters. A time-domain implementation is presented, and important time iteration aspects are reviewed. New formulations for perfectly matched layers and waveguide ports are introduced. An unconditionally stable RPIM scheme is summarized, and its advantages for hybridization with the classical RPIM scheme are discussed in a practical example. The capabilities of an adaptive time-domain refinement strategy based on the experiences on a frequency-domain solver are discussed.</p>}},
  author       = {{Kaufmann, Thomas and Yu, Y. and Engström, C. and Chen, Z. and Fumeaux, C.}},
  issn         = {{0894-3370}},
  keywords     = {{adaptive refinement; collocation method; meshless methods; radial basis function; radial point interpolation method; time domain; unconditional stability}},
  language     = {{eng}},
  number       = {{5-6}},
  pages        = {{468--489}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{International Journal of Numerical Modelling: Electronic Networks, Devices and Fields}},
  title        = {{Recent developments of the meshless radial point interpolation method for time-domain electromagnetics}},
  url          = {{http://dx.doi.org/10.1002/jnm.1830}},
  doi          = {{10.1002/jnm.1830}},
  volume       = {{25}},
  year         = {{2012}},
}