Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions

  • Mahadevan GaneshEmail author
  • Stuart C. Hawkins


In this review article, we describe some advances in applications of the hyperinterpolation operator introduced by Sloan about two decades ago (J Approx Theory 83:238–254, 1995). In particular, our focus is on reviewing the application of the scalar and vector-valued hyperinterpolation approximations for developing, analyzing and implementing fully-discrete high-order algorithms. Such approximations facilitate efficient simulation of scattering of acoustic, electromagnetic and elastic waves, exterior to connected and disconnected bounded three dimensional domains. The main contributions of this article are: (1) a unified (acoustic, electromagnetic, and elastic) approach for the three important classes of waves; (2) theoretical and numerical comparisons of the hyperinterpolation approximations in these three applications; and (3) new results for a class of unbounded heterogeneous media.



Part of this work was carried out while MG was a Visiting Professorial Fellow at University of New South Wales (UNSW) in 2016, funded by an Australian Research Council (ARC) grant. Support of the ARC and the Colorado Golden Energy Computing Organization (GECO) are gratefully acknowledged.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics & StatisticsColorado School of MinesGoldenUSA
  2. 2.Department of MathematicsMacquarie UniversitySydneyAustralia

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