Parallel LOD-FDTD Method With Error-Balancing Properties

We present an improved version of the locally-one-dimensional finite-difference time-domain method in 2-D formulation, featuring spatial expressions derived by an error-amending procedure. The latter targets at the balanced treatment of space-time flaws, and assures the efficient exploitation of four-point spatial operators that now depend on the time-step size. Simulations are also shortened by implementing the algorithm on graphics processing units, a process that necessitates the incorporation of a parallelizable implicit solver. This is accomplished by adapting parallel cyclic reduction to heptadiagonal systems. Therefore, a reliable computational framework free of time-step restrictions is developed.