一种2型三角剖分上多元样条拟插值的精度提高策略

Accuracy Raising Technique for Multivariate Spline Quasi-Interpolants over Type-2 Triangulations

中文关键词:  拟插值  多项式再生  多元样条  数值解

英文关键词:quasi-interpolation  polynomial reproduction  multivariate spline  numerical solution

中文摘要:

      给定一个多元拟插值算子, 若其具有单位分解性质 (再生0次多项式), 我们提出一种利用其周围节点提高多项式再生性的方法. 所得算子不仅具有更高的逼近精度, 还不需要目标函数的任何导数信息. 然后利用此方法, 我们改进了2型三角剖分上的多元样条拟插值，使之具有更高的精度. 最后, 我们应用改进的拟插值算子数值求解时间发展偏微分方程. 数值实验验证了该方法的有效性.

英文摘要:

      Given a multivariate quasi-interpolation operator with the partition of unity property, we propose a method to raise the accuracy with simple knots. The resulting operators possess higher accuracy while not requiring any derivative information of the underlying function. On that basis, we improve the multivariate spline quasi-interpolants with higher accuracy over type-2 triangulations. Moreover, we apply the improved quasi-interpolants to simulate time developing partial differential equations (PDEs). The numerical experiments verify the efficiency of the proposed methods.