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    ARTICLE

    Optimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian Problems

    Chein-Shan Liu1, Chung-Lun Kuo1, Chih-Wen Chang2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 3189-3208, 2024, DOI:10.32604/cmes.2023.046002

    Abstract To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQ-RBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by the MQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and,… More >

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