Development of a multigrid FDTD code for three-dimensional applications

Numerical modeling of realistic engineering problems using the finite-difference time-domain (FDTD) technique often requires more detail than is possible when using a uniform-grid FDTD code. We describe the development of a three-dimensional (3-D) multigrid FDTD code that focuses a large number of cells of small dimensions in the region of interest. The detailed solution procedure is described and some test geometries are solved using both a uniform-grid and the developed multigrid FDTD code to validate the results and check the accuracy of the solution. Results from these comparisons as well as comparisons between the new FDTD code and another available multigrid code are presented. In addition, results from the simulation of realistic microwave-sintering experiments in large multimode microwave cavities are given to illustrate the application of the developed method in modeling electrically large geometries. The obtained results show improved resolution in critical sites inside the 3-D multimode sintering cavity while keeping the required computational resources manageable. It is shown that it is possible to simulate the sintering of ceramic samples of 0.318-cm wall thickness in a cylindrical multimode microwave cavity with a diameter of 74 cm and a length of 112 cm using 2.24×10⁶ total FDTD cells. For comparison, a total of 102×10⁶ cells would have been required if a uniform-grid code with the same resolution had been used