A new 9-point sixth-order accurate compact finite-difference method for the Helmholtz equation
A new 9-point sixth-order accurate compact finite-difference method for the Helmholtz equation
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DOI：
10.1016/j.jsv.2007.06.070
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发表时间：
2007-11
影响因子：
4.7
通讯作者：
M. Nabavi;M. Siddiqui;J. Dargahi
中科院分区：
文献类型：
--
作者：
M. Nabavi;M. Siddiqui;J. Dargahi
本文提出了一种求解一维和二维Helmholtz方程的新的九点六阶精度紧致差分方法。该方案是基于从亥姆霍兹方程计算的导数的六阶近似。一个六阶精度对称表示的诺依曼边界条件也开发。通过对两个具有精确解的试验问题的求解，验证了该方法的有效性和准确性。数值结果表明，该六阶格式具有预期的精度，且对波数具有鲁棒性。
A new 9-point sixth-order accurate compact finite-difference method for solving the Helmholtz equation in one and two dimensions, is developed and analyzed. This scheme is based on sixth-order approximation to the derivative calculated from the Helmholtz equation. A sixth-order accurate symmetrical representation for the Neumann boundary condition was also developed. The efficiency and accuracy of the scheme is validated by its application to two test problems which have exact solutions. Numerical results show that this sixth-order scheme has the expected accuracy and behaves robustly with respect to the wave number.