UCLA

The finite difference time domain method has long been one of the most widely used numerical methods for solving Maxwell’s equations due in part to its accuracy, explicit nature, and simplicity of implementation. Modern research interests have created a need for this method to be extended to handle multi-scale multi-physics problems where numerous physical phenomena are coupled with classical electrodynamics. These phenomena typically occur on vastly different spatial scales; however, the conventional finite difference time domain method requires a uniform spatial discretization across the entire simulation space. Additionally, the maximum time evolution that may be solved in a single iteration of the algorithm is proportional to the smallest discretization length. Consequently, properly resolving the smallest feature of a multiscale problem causes phenomena of a larger scale to be over-resolved, resulting in an unnecessarily large amount of memory and often an impractical number of computations required for simulation. The development of a capability for sub-gridding, where local domains of fine resolution may be incorporated into a simulation space of coarser resolution, is imperative to treat this issue. This thesis proposes a new algorithm to implement sub-gridding. The results of comprehensive numerical evaluations show promise for this algorithm to be of general use in solving multi-scale multi-physics problems.