Static condensation, partial orthogonalization of basis functions, and ILU preconditioning in the hp-FEM

  • Authors:

  • Tomáš Vejchodský;Pavel Šolín

  • Affiliations:

  • Institute of Mathematics, Czech Academy of Sciences, itná 25, 11567 Prague 1, Czech Republic;Institute of Thermomechanics, Czech Academy of Sciences, Dolejškova 5, 182 00 Prague 8, Czech Republic and Department of Mathematical Sciences, University of Texas at El Paso, TX 79968, USA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

Static condensation of internal degrees of freedom, partial orthogonalization of basis functions, and ILU preconditioning are techniques used to facilitate the solution of discrete problems obtained in the hp-FEM. This paper shows that for symmetric linear (not necessarily positive-definite) problems, under mild technical assumptions, these three techniques are completely equivalent. In fact, the same matrices can be obtained by the same arithmetic operations. The study can be extended to nonsymmetric problems naturally.