Published

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

Journal of Scientific Computing, 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.