TY - JOUR AU - Ghaffar, Fazal AU - Badshah, Noor AU - Islam, Saeed AU - Khan, Muhammad Altaf PY - 2016 DA - 2016/01/25 TI - Multigrid method based on transformation-free high-order scheme for solving 2D Helmholtz equation on nonuniform grids JO - Advances in Difference Equations SP - 19 VL - 2016 IS - 1 AB - 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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-016-0745-2 DO - 10.1186/s13662-016-0745-2 ID - Ghaffar2016 ER -