Preconditioning for heterogeneous problems

Sergey V. Nepomnyaschikh, Eun Jae Park

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The main focus of this paper is to suggest a domain decomposition method for mixed finite element approximations of elliptic problems with anisotropic coefficients in domains. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used for a priori estimates of the stability with respect to boundary conditions, and also play very important role in constructing and studying effective domain decomposition methods. The trace theorem for anisotropic rectangles with anisotropic grids is the main tool in this paper to construct domain decomposition preconditioners.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Scienceand Engineering
Pages415-422
Number of pages8
Volume40
Publication statusPublished - 2005 Dec 1

Publication series

NameLecture Notes in Computational Science and Engineering
Volume40
ISSN (Print)1439-7358

Fingerprint

Domain decomposition methods
Preconditioning
Domain Decomposition Method
Sobolev spaces
Trace Theorem
Boundary value problems
Partial differential equations
Mixed Finite Elements
Boundary conditions
Domain Decomposition
A Priori Estimates
Finite Element Approximation
Decomposition
Theorem
Preconditioner
Elliptic Problems
Rectangle
Sobolev Spaces
Partial differential equation
Boundary Value Problem

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Nepomnyaschikh, S. V., & Park, E. J. (2005). Preconditioning for heterogeneous problems. In Domain Decomposition Methods in Scienceand Engineering (Vol. 40, pp. 415-422). (Lecture Notes in Computational Science and Engineering; Vol. 40).
Nepomnyaschikh, Sergey V. ; Park, Eun Jae. / Preconditioning for heterogeneous problems. Domain Decomposition Methods in Scienceand Engineering. Vol. 40 2005. pp. 415-422 (Lecture Notes in Computational Science and Engineering).
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Nepomnyaschikh, SV & Park, EJ 2005, Preconditioning for heterogeneous problems. in Domain Decomposition Methods in Scienceand Engineering. vol. 40, Lecture Notes in Computational Science and Engineering, vol. 40, pp. 415-422.

Preconditioning for heterogeneous problems. / Nepomnyaschikh, Sergey V.; Park, Eun Jae.

Domain Decomposition Methods in Scienceand Engineering. Vol. 40 2005. p. 415-422 (Lecture Notes in Computational Science and Engineering; Vol. 40).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Nepomnyaschikh SV, Park EJ. Preconditioning for heterogeneous problems. In Domain Decomposition Methods in Scienceand Engineering. Vol. 40. 2005. p. 415-422. (Lecture Notes in Computational Science and Engineering).