Acceleration of the 3D ADI-FDTD method using graphics processor units

We present preliminary results of the acceleration of the three-dimensional (3D) alternating direction implicit finite-difference time-domain (ADI-FDTD) method on graphics processor units (GPUs). Although the ADI-FDTD iteration comprises two substeps, which each require solving a tridiagonal matrix system of equations over xy, xz, yz planes of the domain, the application of this scheme frees the time-step size from the Courant-Friedrichs-Lewy stability constraint. In our implementation we took advantage of the fine-grain thread parallelism and coarse-grained block parallelism of the GPU architecture, allowing us to use the parallel cyclic reduction method to simultaneously solve many tridiagonal systems of equations. We obtained a satisfactory speedup of the method indicating that GPUs represent an inexpensive source of computational power for accelerated ADI-FDTD simulations.