The single-grid multilevel method and its applications

Research output: Contribution to journalArticle

Abstract

In this paper, we propose the single-grid multilevel (SGML) method for large-scale linear systems discretized from partial differential equations. The SGML method combines the methodologies of both the geometric and the algebraic multigrid methods. It uses the underlying geometric information from the finest grid. A simple and isotropic coarsening strategy is applied to explicitly control the complexity of the hierarchical structure, and smoothers are chosen based on the property of the model problem and the underlying grid information to complement the coarsening and maintain overall efficiency. Additionally, the underlying grid is used to design an efficient parallel algorithm in order to parallelize the SGML method. We apply the SGML method on the Poisson problem and the convection diffusion problem as examples, and we present the numerical results to demonstrate the performance of the SGML method.

Original languageEnglish (US)
Pages (from-to)987-1005
Number of pages19
JournalInverse Problems and Imaging
Volume7
Issue number3
DOIs
StatePublished - Aug 1 2013

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Multilevel Methods
Coarsening
Grid
Parallel algorithms
Partial differential equations
Linear systems
Algebraic multigrid Method
Poisson Problem
Convection-diffusion Problems
Large-scale Systems
Hierarchical Structure
Parallel Algorithms
Efficient Algorithms
Complement
Partial differential equation
Linear Systems
Numerical Results
Convection
Methodology

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

Cite this

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The single-grid multilevel method and its applications. / Xu, Jinchao.

In: Inverse Problems and Imaging, Vol. 7, No. 3, 01.08.2013, p. 987-1005.

Research output: Contribution to journalArticle

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