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Journal of Scientific Computing

Erschienen in:

05.03.2016

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

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

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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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.

Vorheriger Artikel High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes

Nächster Artikel Modified Gauss–Laguerre Exponential Fitting Based Formulae

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Titel: Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems
verfasst von: Bin Zheng
Luoping Chen
Xiaozhe Hu
Long Chen
Ricardo H. Nochetto
Jinchao Xu
Publikationsdatum: 05.03.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0189-6

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