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Stephen D. Bond

Citation:

Burak Aksoylu, Michael Holst and Stephen Bond, Implementation and Theoretical Aspects of the BPX Preconditioner in the Three Dimensional Local Mesh Refinement Setting, Institute for Computational Engineering and Sciences, The University of Texas at Austin:ICES Technical Report 04-50, October (2004).

Abstract:

In the setting of 3D local mesh refinement, we present the theoretical construction and the implementation aspects of the Bramble-Pasciak-Xu (BPX) preconditioner. The refinement under consideration is the 3D local red-green refinement procedure introduced by Bornemann-Erdmann-Kornhuber (BEK). We outline how to construct the theoretical optimality of the BPX preconditioner in the setting of elliptic second order PDEs. Hence, the resulting BPX preconditioner for the BEK refinement setting has provably optimal (linear) computational complexity per iteration, as well as having a uniformly bounded condition number. We provide detailed comparisons of the BPX preconditioner to hierarchical basis (HB) and wavelet modified HB preconditioners including the flop counts. Numerical experiments in 2D are presented for both the additive and multiplicative versions of the above preconditioners.

Full Text:

ICES Report 04-50

Preprint:

Implementation and Theoretical Aspects of the BPX Preconditioner in the Three Dimensional Local Mesh Refinement Setting (272K, PDF)

Bibtex:
@article{AHB2004,
  author  = {Burak Aksoylu and Michael Holst and Stephen Bond},
  title   = {Implementation and Theoretical Aspects of the BPX Preconditioner
             in the Three Dimensional Local Mesh Refinement Setting},
  institution = {Institute for Computational Engineering and Sciences, The
             University of Texas at Austin},
  number  = {ICES Technical Report 04-50},
  month   = {October},
  year    = 2004,
  url     = {http://www.ices.utexas.edu/research/reports/2004/0450.pdf}
}

Stephen Bond