Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates (Communications in Computational Physics, 2018)
This paper presents new finite difference schemes for solving the Helmholtzequation in the polar and spherical coordinates. The most important result presentedin this study is that the developed difference schemes are pollution free, and theirconvergence orders are independent of the wave number k. Let h denote the stepsize, it will be demonstrated that when solving the Helmholtz equation at large wavenumbers and considering kh is fixed, the errors of the proposed new schemes decreaseas h decreases even when k is increasing and kh>1.