Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

Bin Zheng, Luoping Chen, Xiaozhe Hu, Long Chen, Ricardo H. Nochetto, Jinchao Xu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.

Original languageEnglish (US)
Pages (from-to)201-226
Number of pages26
JournalJournal of Scientific Computing
Volume69
Issue number1
DOIs
StatePublished - Oct 1 2016

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Parabolic Problems
Preconditioner
Fourth Order
Discretization
Eigenvalue Analysis
Finite element method
Iterative Solvers
Fourth-order Equations
Mixed Finite Element Method
Diffusion Coefficient
Parabolic Equation
Rate of Convergence
Numerical Examples
Class
Estimate

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Zheng, Bin ; Chen, Luoping ; Hu, Xiaozhe ; Chen, Long ; Nochetto, Ricardo H. ; Xu, Jinchao. / Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems. In: Journal of Scientific Computing. 2016 ; Vol. 69, No. 1. pp. 201-226.
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Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems. / Zheng, Bin; Chen, Luoping; Hu, Xiaozhe; Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao.

In: Journal of Scientific Computing, Vol. 69, No. 1, 01.10.2016, p. 201-226.

Research output: Contribution to journalArticle

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