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    An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem

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    Access Status
    Open access
    Authors
    Wang, Song
    Date
    2018
    Type
    Journal Article
    
    Metadata
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    Citation
    Wang, S. 2018. An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem. Applied Mathematical Modelling. 58: pp. 217-228.
    Source Title
    Applied Mathematical Modelling
    DOI
    10.1016/j.apm.2017.07.038
    ISSN
    0307-904X
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/66879
    Collection
    • Curtin Research Publications
    Abstract

    We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equation containing a penalty function with a penalty parameter µ > 0. The penalty equation is shown to be uniquely solvable. We also prove that the solution to the penalty equation converges to the exact one at the rate O(µ 1/2 ) as µ ? 0. A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Numerical experiments, performed on some non-trivial test examples, demonstrate the computed rate of convergence matches the theoretical one.

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