Overview of the Unconditionally Stable Weighted Laguerre Polynomials FDTD method

This overview introduces the unconditionally stable Weighted Laguerre Polynomials (WLP) finite-difference time-domain (FDTD) method, briefly calling it the WLP-FDTD method. The main characteristic for this method is that it adopts a marching-on-in-order scheme, which respectively uses the WLP functions as temporal expansions and testing functions to expand and solve Maxwell’s equations in a finite dimensional algebra domain. Here, we review it with some developments in WLP-FDTD method into the four principal aspects, basic algorithm, efficient algorithm, hybrid algorithm and applications, which can be considered as a time-frequency solver for Maxwell equation, reducing the computational time considerably, at the same time, the accuracy of traditional FDTD method is equal to the FDTD method.