maxwell equation cylindrical coordinates

The time-domain Maxwell equations in cylindrical coordinates are transformed to AH domain using a AH differential operator technology. Here, we extend the AH FDTD method to cylindrical coordinates system to analyze this case. In many applications, such as EM ground wave propagation from a lightning channel, a cylindrical coordinate is preferred. For the latter, all of the works are based on in Cartesian grid previously. The former is based on weighted Laguerre polynomials (WLP), and the latter is based on associated Hermite (AH) functions. The orthogonal function-based methods can be classified into two main categories: the marching-on-in-order scheme and the paralleling-in-order scheme. To eliminate the stability condition for fine structure, many unconditionally stable (US) methods were proposed, such as alternating direction implicit (ADI) method and orthogonal function-based methods. So for the problems with fine structures, it should choose a small time step and then a large number of marching-on-in-time steps for simulation, which is a time-consuming process. In the finite-difference time-domain (FDTD) method, the time step size is limited by the Courant-Friedrich-Levy (CFL) stability condition. The numerical results represent the accuracy and efficiency of the proposed method when comparing for the conventional FDTD method. With AH domain differentiate operator technology and paralleling-in-order solution scheme, the cylindrical time-domain Maxwell equations with complex frequency shifted perfectly matched layer (CFS-PML) are transformed to AH domain generating a five-point banded equation, which also unified the formula from the central axis of cylinder. The latter describes the density and flux of energy and momentum in spacetime.We extended the unconditionally stable associated Hermite (AH) FDTD method to the cylindrical coordinate system for analyzing the electromagnetic (EM) ground wave propagation. In the relativistic formulation of electromagnetism, the Maxwell's tensor appears as a part of the electromagnetic stress–energy tensor which is the electromagnetic component of the total stress–energy tensor. It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand. When the situation becomes more complicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force law. The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum.

Maxwell equation cylindrical coordinates