On element-by-element preconditioning for general elliptic problems
Generate an AI Snapshot to get a quick, structured summary of this paper.
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Analysis of the efficiency of element-by-element preconditioning to problems with discontinuous variable coefficients on regular grids in two and three dimensions and to constant coefficient two-dimensional problems on elements with variable aspect ratio is extended.
Abstract
Iterative solution procedures for finite element equations become competitive with widely used direct techniques particularly for large three-dimensional problems when computer storage and time are limited. The conjugate gradient method has attractive theoretical properties and is especially efficient when a good preconditioner is used. The efficiency of element-by-element preconditioning has previously been investigated by the second author on model constant coefficient problems on regular grids in two and three dimensions. In this paper we extend that analysis to problems with discontinuous variable coefficients on regular grids in two and three dimensions and to constant coefficient two-dimensional problems on elements with variable aspect ratio.