Accuracy of staircase approximations in finite-difference methods for wave propagation (Q478099)

The paper deals with the numerical solution of 2D wave equation with the aid of the Yee (finite difference) method. The main drawback of the method is the use of staircase boundary approximations, which leads to inconsistent results. In this paper, the authors derive exact discrete solutions to the Yee scheme close to the staircase approximated boundary, enabling a detailed theoretical study of the amplitude, phase and frequency errors created. Furthermore, they show how evanescent waves of amplitude \(O(1)\) occur along the boundary. The detailed numerical analysis is presented and numerical examples are included.