论文标题
高阶最大透镜搭配方法
High-order maximum-entropy collocation methods
论文作者
论文摘要
本文考虑了基于高阶局部最大渗透方案（HOLMES）的点搭配框架的部分微分方程的近似。在这种方法中，通过优化程序计算平滑的基础函数，并且在搭配点直接施加了问题的强大形式，从而大大减少了相对于Galerkin公式的计算时间。此外，这种方法确实是无网状的，因为不需要背景集成网格。用支持性的数值示例验证了所提出方法的有效性，其中获得了预期的收敛速率。这包括在由隐式和显式（NURB）曲线界定的域上的PDE近似，说明了几何建模与数值分析之间的直接整合。
This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an optimization procedure and the strong form of the problem is directly imposed at the collocation points, reducing significantly the computational times with respect to the Galerkin formulation. Furthermore, such a method is truly meshless, since no background integration grids are necessary. The validity of the proposed methodology is verified with supportive numerical examples, where the expected convergence rates are obtained. This includes the approximation of PDEs on domains bounded by implicit and explicit (NURBS) curves, illustrating a direct integration between the geometric modeling and the numerical analysis.
