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  • 1.
    Kaufmann, T.
    et al.
    University of Adelaide, Australia.
    Yu, Y.
    Dalhousie University, Canada.
    Engström, Christian
    ETH Zurich, Switzerland.
    Chen, Z.
    Dalhousie University, Canada.
    Fumeaux, C.
    University of Adelaide, Australia.
    Recent developments of the meshless radial point interpolation method for time‐domain electromagnetics2012In: International journal of numerical modelling, ISSN 0894-3370, E-ISSN 1099-1204, Vol. 25, no 5-6, p. 468-489Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Kaufmann, Thomas
    et al.
    University of Adelaide, Australia.
    Engström, Christian
    Umeå university, Sweden.
    High-order absorbing boundary conditions for the meshless radial point interpolation method in the frequency domain2013In: International journal of numerical modelling, ISSN 0894-3370, E-ISSN 1099-1204, Vol. 26, no 5, p. 478-492Article in journal (Refereed)
    Abstract [en]

    The meshless radial point interpolation method (RPIM) in frequency domain for electromagnetic scattering problems is presented. This method promises high accuracy in a simple collocation approach using radial basis functions. The treatment of high-order non-reflecting boundary conditions for open waveguides is discussed and implemented up to fourth-order. RPIM allows the direct calculation of high-order spatial derivatives without the introduction of auxiliary variables. High-order absorbing boundary conditions offer a choice of absorbing angles for each degree of spatial derivatives. For general applications, a set of these absorbing angles is calculated using global optimization. Numerical experiments show that at the same computational cost, the numerical reflections of the absorbing boundary conditions are much lower than conventional perfectly matched layers, especially at high angles of incidence.

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