The orthogonal expansion based unconditionally stable FDTD method has been developed and attracted much attention recently. It can be implemented by two schemes: marching-on-in-order and paralleling-in-order solution, which respectively use weighted Laguerre polynomials (WLP) and associated Hermite (AH) functions as temporal expansions and testing functions. This paper proposed to use Legendre polynomials as another kind of orthogonal basis to make a new paralleling-in-order based unconditionally stable FDTD method. Numerical result shows it has much better performance in long time simulation case when compared with AH FDTD method.
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