Orthogonal spline collocation is implemented for the numerical solution of two‐dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost of O(N² log N) on an N × N partition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers.

中文翻译：

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带界面的二维亥姆霍兹问题的四阶正交样条搭配方法

正交样条搭配用于二维Helmholtz问题的数值解，单位平方中的系数不连续。矩阵分解算法用于在单位正方形的N  ×  N分区上以O（N ²  log  N）的代价求解搭配矩阵系统。数值实验的结果证明了这种方法的有效性，在各种范数和超收敛现象中展示了最佳的全局估计，适用于广谱波数。