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    The Scalar Homotopy Method for Solving Non-Linear Obstacle Problem

    Chia-Ming Fan1,2, Chein-Shan Liu3, Weichung Yeih1, Hsin-Fang Chan1

    CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 67-86, 2010, DOI:10.3970/cmc.2010.015.067

    Abstract In this study, the nonlinear obstacle problems, which are also known as the nonlinear free boundary problems, are analyzed by the scalar homotopy method (SHM) and the finite difference method. The one- and two-dimensional nonlinear obstacle problems, formulated as the nonlinear complementarity problems (NCPs), are discretized by the finite difference method and form a system of nonlinear algebraic equations (NAEs) with the aid of Fischer-Burmeister NCP-function. Additionally, the system of NAEs is solved by the SHM, which is globally convergent and can get rid of calculating the inverse of Jacobian matrix. In SHM, by introducing a scalar homotopy function and… More >

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