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

Advances in Difference Equations

Noor Badshah¹  Saeed Islam²  Muhammad Altaf Khan²  Fazal Ghaffar² 

[1] Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan;Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan

关键词: Helmholtz equation;    compact iterative schemes;    multigrid method;    nonuniform grids;    65Nxx;    65Mxx;   

DOI  :  10.1186/s13662-016-0745-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY