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A matrix triangularization algorithm for the polynomial point interpolation method

机译：多项式点插值方法的矩阵三角化算法

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摘要

A novel matrix triangularization algorithm (MTA) is proposed to overcome the singularity problem in the point interpolation method (PIM) using the polynomial basis, and to ensure stable and reliable construction of PIM shape functions. The present algorithm is validated using several examples, and implemented in the local point interpolation method (LPIM) that is a truly meshfree method based on a local weak form. Numerical examples demonstrate that LPIM using the present MTA are very easy to implement, and very robust for solving problems of computational mechanics. It is shown that PIM with the present MTA is very effective in constructing shape functions. Most importantly, PIM shape functions possess Kronecker delta function properties. Parameters that influence the performance of them are studied in detail. The convergence and efficiency of them are thoroughly investigated.
机译：提出了一种新颖的矩阵三角化算法（MTA），以解决基于多项式的点插值法（PIM）中的奇异性问题，并确保稳定可靠地构造PIM形状函数。本算法使用几个示例进行了验证，并以局部点插值方法（LPIM）实施，该方法是一种基于局部弱形式的真正无网格方法。数值示例表明，使用本MTA的LPIM非常易于实现，并且对于解决计算力学问题非常强大。结果表明，采用本MTA的PIM在构造形状函数方面非常有效。最重要的是，PIM形状函数具有Kronecker增量函数属性。对影响它们性能的参数进行了详细研究。他们的收敛性和效率已被彻底研究。

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