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A fourth–order orthogonal spline collocation method for two‐dimensional Helmholtz problems with interfaces
Numerical Methods for Partial Differential Equations ( IF 2.1 ) Pub Date : 2020-07-17 , DOI: 10.1002/num.22505 Santosh Kumar Bhal 1 , Palla Danumjaya 1 , Graeme Fairweather 2
Numerical Methods for Partial Differential Equations ( IF 2.1 ) Pub Date : 2020-07-17 , DOI: 10.1002/num.22505 Santosh Kumar Bhal 1 , Palla Danumjaya 1 , Graeme Fairweather 2
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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:
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。
更新日期:2020-07-17
中文翻译:
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。