Multigrid method based on transformation-free high-order scheme for solving 2D Helmholtz equation on nonuniform grids

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• 作者：Fazal Ghaffar ; Noor Badshah ; Saeed Islam…
• 关键词：65Nxx ; 65Mxx ; Helmholtz equation ; compact iterative schemes ; multigrid method ; nonuniform grids
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：2,337 KB
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• 作者单位：Fazal Ghaffar (1)
  Noor Badshah (2)
  Saeed Islam (1)
  Muhammad Altaf Khan (1)
  
  1. Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
  2. Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

High-order compact difference schemes can achieve higher-order accuracy on uniform grids. However, in some cases these may not achieve the desired accuracy. Therefore, we propose a multigrid method based on high-order compact difference scheme on nonuniform grids. We will use interpolation and restriction operators developed by Ge and Cao (J. Comput. Phys. 230:4051-4070, 2011). The suggested scheme has up to fourth-order accuracy. Lastly, some numerical experiments are given to show the accuracy and performance of the proposed scheme. Keywords Helmholtz equation compact iterative schemes multigrid method nonuniform grids