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IMPLEMENTATION AND THEORETICAL ASPECTS OF THE BPX PRECONDITIONER IN THE THREE DIMENSIONAL
 

Summary: IMPLEMENTATION AND THEORETICAL ASPECTS OF THE
BPX PRECONDITIONER IN THE THREE DIMENSIONAL
LOCAL MESH REFINEMENT SETTING
BURAK AKSOYLU, MICHAEL HOLST, AND STEPHEN BOND
Abstract. In the setting of 3D local mesh refinement, we present the theoret-
ical 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 result-
ing 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 precondi-
tioners including the flop counts. Numerical experiments in 2D are presented
for both the additive and multiplicative versions of the above preconditioners.
1. Introduction
In this article, we present the theoretical construction and the implementation
aspects of the well-known Bramble-Pasciak-Xu (BPX) preconditioner. The BPX
preconditioner is the parallelized or additive version of the multigrid preconditioner.

  

Source: Aksoylu, Burak - Center for Computation and Technology & Department of Mathematics, Louisiana State University
Bond, Stephen - Department of Computer Science, University of Illinois at Urbana-Champaign
Holst, Michael J. - Department of Mathematics, University of California at San Diego

 

Collections: Computer Technologies and Information Sciences; Mathematics