Simulations of the Helmholtz equation at any wave number for adaptive grids using a modified central finite difference scheme

Authors : Hafiz Abdul Wajid

Pages : 806-815

View : 10 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain. A variety of numerical examples are considered to validate the superiority of the modified scheme for a nonuniform grid over a standard central finite difference scheme.
Keywords : Helmholtz equation, modified central finite difference scheme, numerical dispersion, nonuniform grids, adaptive grids