In the current study, we propose an accurate numerical method for plane elastostatic equations of anisotropic functionally graded materials. The proposed method uses radial basis functions augmented with polynomial basis functions in a collocation framework by employing ghost point centers which cover physical domain of considered problem. Unlike in classical collocation approach where the centers and collocation points are taken identically, using ghost centers different from the collocation points greatly improves the accuracy of the proposed method. Addition of polynomial basis function to the radial basis functions stabilized the method against shape parameter of radial basis functions and also increases accuracy of solution, mostly. Some numerical examples are solved via the proposed method both on regular and irregular domains. L∞, L2 and RMS error norms are calculated and for sufficient number of collocation points their values are smaller than 1e−10. The obtained error norms and their comparison with other methods available in literature confirm precision of the suggested numerical method.

中文翻译：

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将多项式增强 RBF 搭配方法与鬼点用于各向异性功能梯度材料的平面弹性方程


在目前的研究中，我们提出了一种用于各向异性功能梯度材料的平面弹性方程的精确数值方法。所提出的方法使用径向基函数，通过采用覆盖所考虑问题的物理域的幽灵点中心，在搭配框架中使用多项式基函数增强。与中心和搭配点相同的经典搭配方法不同，使用与搭配点不同的幽灵中心大大提高了所提方法的准确性。在径向基函数中加入多项式基函数稳定了该方法对径向基函数形状参数的影响，并在很大程度上提高了求解的准确性。通过所提出的方法在规则域和不规则域上求解了一些数值示例。计算 L∞、L2 和 RMS 误差范数，对于足够数量的配置点，它们的值小于 1e-10。获得的误差范数及其与文献中可用的其他方法的比较证实了所建议的数值方法的精确性。