期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates
下载PDF
导出
摘要 We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions. We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.
作者 Na Zhu Meiling Zhao
机构地区 School of Mathematics and Physics
出处 《American Journal of Computational Mathematics》 2019年第3期174-186,共13页 美国计算数学期刊（英文）
关键词 HIGH-ORDER HELMHOLTZ EQUATION POLAR COORDINATES High-Order Helmholtz Equation Polar Coordinates
分类号 O1 [理学—基础数学]
  • 相关文献

参考文献1

二级参考文献15

  • 1I. Harari, E. Turkel. Accurate finite difference methods for time-harmonic wave propagation , J. Comput. Phy., 119 (1995), 252-270.
  • 2I. Singer, E. Turkel. High-order finite difference methods for the Helmholtz equation, Comput. Meth. Appl. Mech. Engrg. 163 (1998), 343-358.
  • 3Majid Nabavi, M. H. Kamran Siddiqui, Javad Dargahi. A new point sixth-order accurate compact finite difference method for the Helmholtz equation, Journal of Sound and Vibration. 307 (2007), 972-982.
  • 4Singer, I., Turkel, E.. Sixth-order accurate finite difference schemes for the Hehnholtz equation, J. Comput. Aeoust., 14 (2006), 339-351.
  • 5Godehard Sutmann. Compact finite difference schemes of sixth order for the Helmholtz equation, J. Comput. App. Math., 203 (2007), 15-31.
  • 6G. Baruch, G. Fibich, S. Tsynkov and E. Turkel, Fourth-order schemes for time-harmonic wave equations with discontinuous coefficients, Commun. Comput. Phys., 5 (2009), 442-455.
  • 7G. Baruch, G. Fibich and S. Tsynkov, High-order numerical method for the nonlinear Helmholtz equation with material discontinuities, J. Comput. Phys., 227 (2007), 820-850.
  • 8R.J. LeVeque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31 (1994), 1019-1044.
  • 9Z. Li and K. Ito, The Immersed Interface Method for Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, SIAM Frontier Series in Applied Mathematics, FR33, 2006.
  • 10S. Britt, S. Tsynkov and E. Turkel, A compact fourth order scheme for the helmholtz equation in polar coordinates, J. Sci. Comput., 45 (2010), 26-47.

共引文献2

American Journal of Computational Mathematics
2019年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部