Superlinear PCG algorithms

Symmetric part preconditioning and boundary conditions

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The discussion relies on suitably developed Hilbert space theory for linear operators.

Original languageEnglish
Pages (from-to)590-611
Number of pages22
JournalNumerical Functional Analysis and Optimization
Volume29
Issue number5-6
DOIs
Publication statusPublished - May 2008

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Superlinear Convergence
Hilbert spaces
Preconditioning
Mathematical operators
Boundary conditions
Finite element method
Mixed Boundary Conditions
Convection-diffusion Equation
Elliptic Problems
Dirichlet Problem
Linear Operator
Hilbert space
Discretization
Mesh
Convection

Keywords

  • Conjugate gradient method
  • Mesh independence
  • Mixed boundary conditions
  • Preconditioning
  • Superlinear convergence
  • Symmetric part

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization

Cite this

Superlinear PCG algorithms : Symmetric part preconditioning and boundary conditions. / Karátson, J.

In: Numerical Functional Analysis and Optimization, Vol. 29, No. 5-6, 05.2008, p. 590-611.

Research output: Contribution to journalArticle

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