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

Authors:
T. Kaufmann;Y. Yu;C. Engström;Z. Chen;C. Fumeaux
Affiliations:
The School of Electrical & Electronic Engineering, University of Adelaide, Adelaide, SA5005, Australia;Department of Electrical and Computer Engineering, Dalhousie University, Halifax, NSCanadaB3J 1Z1;Laboratory for Electromagnetic Fields and Microwave Electronics (IFH), ETH Zurich, Gloriastrasse 35, 8092, Zurich, Switzerland;Department of Electrical and Computer Engineering, Dalhousie University, Halifax, NSCanadaB3J 1Z1;The School of Electrical & Electronic Engineering, University of Adelaide, Adelaide, SA5005, Australia
Venue:
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Year:
2012

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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 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. Copyright © 2012 John Wiley & Sons, Ltd.