Unconditionally Stable MFLTD Method for the Full Wave Electromagnetic Simulation

A new unconditionally stable numerical method for the time domain simulation of electromagnetic problems using a combination of the Laguerre polynomials in the time domain and radial basis functions (RBF) in the spatial domain named mesh-Free Laguerre time domain (MFLTD) method is described. Unconditionally stable Laguerre based method may be computationally much more efficient than the FDTD methods and using RBFs allows computing the problems with complex-shapes in a non-uniform point's distribution. A numerical example at the final part of the communication shows the efficiency of the presented method in problems with sparse and coarse regions. Using the MFLTD method for this example, we can achieve a 96% reduction in the computation time and get an acceptable degree of accuracy in comparison to the conventional mesh-free time-domain (MFTD) method.