A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions

Luca F. Pavarino, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems. A p-version finite element method based on continuous, piecewise Qp functions is considered for second-order elliptic problems in three dimensions; this special method can also be viewed as a conforming spectral element method. An iterative method is designed for which the condition number of the relevant operator grows only in proportion to ( 1 + log p)2. This bound is independent of jumps in the coefficient of the elliptic problem across the interfaces between the subregions. Numerical results are also reported which support the theory.

Original languageEnglish (US)
Pages (from-to)1303-1335
Number of pages33
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number4
StatePublished - Aug 1996

Fingerprint

Iterative Substructuring
Spectral Elements
Iterative methods
Three-dimension
P-version
Spectral Element Method
Second-order Elliptic Problems
Piecewise continuous
Decomposition Algorithm
Domain Decomposition
Condition number
Elliptic Problems
Jump
Proportion
Finite Element Method
Finite Element
Decomposition
Iteration
Finite element method
Numerical Results

Keywords

  • Domain decomposition
  • Iterative substructuring
  • p-version finite elements
  • Spectral approximation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions. / Pavarino, Luca F.; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 33, No. 4, 08.1996, p. 1303-1335.

Research output: Contribution to journalArticle

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