Fundamental Weaker HIE-PML Algorithm With Simple Implementation and Enlarged Time Step for Fine Details Along a Single Direction

Hybrid implicit–explicit (HIE) algorithm is regarded as a powerful method to analyze structures with fine details along a single direction. Here, fundamental weaker HIE (WHIE) algorithm is proposed with the advantages of simple implementation and enlarged time step. Through the employment of the fundamental scheme, the simplest form can be obtained at the right side of the update equations, which avoids the calculation of matrices. Based on the weaker stability condition, time step can be further enlarged compared with the other implicit schemes. Higher order perfectly matched layer (PML) formulation is introduced based on the proposed algorithm to terminate unbounded domains. To validate the algorithm, numerical examples are carried, which include the classical half-space ground-penetrating radar (GPR) problem, magic-T waveguide problem, and periodic metamaterial problem. Through the results, the proposed fundamental HIE algorithm behaviors improvement in efficiency and resources. In addition, absorption shows significant enhancement according to the fundamental higher order formulation by further absorbing the low-frequency propagation waves, evanescent waves, and late-time reflections.