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Mathematical Problems in Engineering
Volume 2016, Article ID 1719846, 16 pages
Research Article

Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation

1School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
2Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
3Department of Mathematics, Foshan University, Foshan 528000, China

Received 3 December 2015; Revised 20 February 2016; Accepted 3 March 2016

Academic Editor: Yan-Wu Wang

Copyright © 2016 Tingting Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML). This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency.