A wavelet based adaptive gridding algorithm for the finite difference time domain method

Abstract

The finite difference time domain (FDTD) method is one of the most popular and powerful numerical techniques in electromagnetic fields simulation. However, it suffers form a limitation that large computational resources are required. It is because the cell size in the solution domain is proportional to the wavelength of the signal under simulation. Therefore, large number of grid points are required when a medium or large structure is excited by a high frequency source. These grid points require large memory to store and lead to long computational time when traditional Yee's FDTD method is used. A wavelet based adaptive non-uniform grid, which depends on the variation of electromagnetic fields, is proposed to apply to the FDTD method. Since most of the simulations use a Gaussian pulse or a modulated Gaussian pulse as the excitation, the electromagnetic fields in most regions of the computational domain are smooth. These regions are over resolved if a fine uniform grid is used. Therefore, the use of adaptive non-uniform grid can reduce the required computational resources by removing unnecessary grid points. The new scheme is applied to analyse several electromagnetic problems, such as a plane wave propagating in a parallel plate waveguide and the scattering of a TM wave on a perfectly conducting rectangular cylinder. It is found that the new scheme can obtain a very accurate result by using only 30%~60% of the computational resources used by the conventional FDTD method.