Efficient parallel solvers for the biharmonic equation

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    We examine the convergence characteristics and performance of parallelised Krylov subspace solvers applied to the linear algebraic systems that arise from low-order mixed finite element approximation of the biharmonic problem. Our strategy results in preconditioned systems that have nearly optimal eigenvalue distribution, which consists of a tightly clustered set together with a small number of outliers. We implement the preconditioner operator in a "black-box" fashion using publicly available parallelised sparse direct solvers and multigrid solvers for the discrete Dirichlet Laplacian. We present convergence and timing results that demonstrate efficiency and scalability of our strategy when implemented on contemporary computer architectures. © 2003 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)35-55
    Number of pages20
    JournalParallel Computing
    Issue number1
    Publication statusPublished - Jan 2004


    • Biharmonic equation
    • Finite elements
    • Krylov solvers
    • Multigrid
    • Preconditioning
    • Sparse direct linear solvers


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