Unconditionally stable locally tridiagonal iterative FDTD for high loss applications

We first show the ADI numerical errors when measured against the Crank-Nicolson scheme are quadratically proportional to both the temporal discretization and lossy values. The ADI method is therefore ineffective for lossy wave propagation simulations requiring larger temporal resolution. Locally tridiagonal iterative methods are then developed to avoid such errors. Standard Jacobi, Gauss-Seidel and Successive Over-Relaxation methods can all be used. In contrast to the ADI method, numerical results demonstrate that the proposed iterative method is extremely effective for high loss problems - reaching a large CFL value limited only by the CN equations.