Improvement of computational performance of implicit finite difference time domain method

Abstract

Different solution techniques, computational aspects and the ways to improve the performance of 3D frequency dependent Crank Nicolson finite difference time domain (FD-CN-FDTD) method are extensively studied here. FD-CN-FDTD is an implicit unconditionally stable method allowing time discretization beyond the Courant-Friedrichs-Lewy (CFL) limit. For the solution of the method both direct and iterative solver approaches have been studied in detail in terms of computational time, memory requirements and the number of iteration requirements for convergence with different CFL numbers (CFLN). It is found that at higher CFLN more iterations are required to converge resulting in increased number of matrix-vector multiplications. Since matrix-vector multiplications account for the most significant part of the computations their efficient implementation has been studied in order to improve the overall efficiency. Also the scheme has been parallelized in shared memory architecture using OpenMP and the resulted improvement of performance at different CFLN is presented. It is found that better speed-up due to parallelization always comes at higher CFLN implying that the use of FD-CN-FDTD method is more appropriate while parallelized.