Parallelisation of Implicit Time Domain Methods: Progress with ADI-FDTD

We provide an overview of our work to date on the parallelization of implicit time domain methods, in particular the alternating direction implicit finite-difference time-domain method (ADI-FDTD). First we describe a domain decomposition scheme for parallel ADI-FDTD in three dimensions that is suitable for implementation on widely available high performance computer architectures such as symmetric multiprocessors (SMP) and distributed memory computer clusters (DMCC). We present a selection of benchmark results for parallel solutions for domains of up to 8 billion mesh cells, and compare against standard parallel FDTD. The results indicate that a useful speed-up can be obtained with ADI-FDTD for large, highly oversampled meshes. We also present a formulation and benchmark results for parallel ADI-Body Of Revolution-FDTD. Our demonstration of parallel speed up represents an important step forward for the application of implicit time domain solvers. We expect that our parallelisation approach can be adopted for related implicit FDTD methods.