A Theoretical Extension of AH FDTD Method and Applications in Various Physical Fields

In this paper, we extended the Associated Hermite (AH) FDTD method theoretically and used it to analyze various physical fields, which are electromagnetic (EM) field, acoustic field, and heat-transfer field. The AH differential transformation operator is developed theoretically as a basic element for setting a time–frequency bridge, where several common operators such as differential, second-order differential, integral linear operator, etc. on the concept of signal processing and analyzing can be expediently transformed, which leads to a unified and much simpler derivation to construct the previous AH FDTD formula. Therefore, it gives a reconsideration for AH FDTD to calculate a more general or even arbitrary liner physic field problems, which are focused on the commonly partial differential equations. Finally, based on the time–frequency bridge theory, we adopted several examples for verification from the formula derivation to numerical validation in EM field, acoustic field, and heat-transfer field, respectively.