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Applications to Finite Element Matrices

  • Wolfgang Hackbusch
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 49)

Abstract

In §9.2.2 it was shown that the matrices arising from finite element discretisations (in what follows called the finite element matrices) are not only sparse but also belong to the \(\mathcal{H}\)-matrix set \(\mathcal{H}(r, P)\) for all \( r \in {_0} \), where P is the standard partition. This allows us to consider all finite element matrices as hierarchical matrices. In particular, no truncation is needed to use a finite element matrix as an input parameter for the inversion or for the LU algorithm.

In Section 11.1 we discuss the inverse of the mass matrix. Using tools from §9.5, we show that the inverse can be approximated by a hierarchical matrix. This result is required in the later analysis.

Section 11.2 is concerned with the continuous and discrete Green operator.

The analysis of the Green function in Section 11.3 yields the \(\mathcal{H}\)-matrix property of the inverse finite element matrix.

The results of this chapter have been improved by recent contributions mentioned in Section 11.4.

Keywords

Green Function Mass Matrix Boundary Element Method Subspace Versus Admissibility Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.MPI für Mathematik in den NaturwissenschaftenLeipzigGermany

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