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Keywords:

  • meshless methods;
  • radial basis function;
  • radial point interpolation method;
  • collocation method;
  • time domain;
  • unconditional stability;
  • adaptive refinement

SUMMARY

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.