A two-dimensional (2D) elliptic problem with nonlocal boundary conditions on both regular and irregular domains is solved numerically by Pascal polynomial basis unified with multiple-scale technique. Very accurate numerical solutions and quite reasonable condition numbers are obtained with the proposed method which is also a truly meshfree method since difficult meshing processes or numerical integrations over domains are not needed for considered problems. Four test problems are solved to show the accuracy and efficiency of the proposed method. Also stability of the method is studied against large noise effect.

中文翻译：

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基于多尺度帕斯卡多项式的非局部边界条件下二维椭圆问题数值解的无网格计算方法

采用多尺度技术统一的帕斯卡多项式基数值求解规则域和不规则域上具有非局部边界条件的二维（2D）椭圆问题。使用所提出的方法获得了非常准确的数值解和相当合理的条件数，这也是一种真正的无网格方法，因为所考虑的问题不需要困难的网格划分过程或域上的数值积分。解决了四个测试问题，以显示所提出方法的准确性和效率。还研究了该方法对大噪声影响的稳定性。