Fast simplicial quadrature-based finite element operators using Bernstein polynomials

  • Authors:

  • Robert C. Kirby;Kieu Tri Thinh

  • Affiliations:

  • Texas Tech University, Department of Mathematics and Statistics, PO Box 1042, 79409-1042, Lubbock, TX, USA;Texas Tech University, Department of Mathematics and Statistics, PO Box 1042, 79409-1042, Lubbock, TX, USA

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2012

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Abstract

We derive low-complexity matrix-free finite element algorithms for simplicial Bernstein polynomials on simplices. Our techniques, based on a sparse representation of differentiation and special block structure in the matrices evaluating B-form polynomials at warped Gauss points, apply to variable coefficient problems as well as constant coefficient ones, thus extending our results in Kirby (Numer Math, 2011, in press).