Fast Summation Techniques for Sparse Shape Functions in Tetrahedral hp-FEM

  • Sven Beuchler
  • Veronika Pillwein
  • Sabine Zaglmayr
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 91)


This paper considers the h p-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in optimal complexity. The algorithm is based on sum factorization and makes use of the nonzero pattern of the stiffness matrix.


Stiffness Matrix Nonzero Entry Jacobi Polynomial Gaussian Point Tetrahedral Element 
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The work has been supported by the FWF projects P20121, P20162, and P23484.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sven Beuchler
    • 1
  • Veronika Pillwein
    • 2
  • Sabine Zaglmayr
    • 3
  1. 1.Institute for Numerical SimulationUniversity BonnBonnGermany
  2. 2.RISCUniversity LinzLinzAustria
  3. 3.CST - Computer Simulation Technology AGDarmstadtGermany

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