A New Efficient ADE-CN-RBF Collocation Meshless Method for Wave Propagation in General Dispersive Meduims

In this paper, we introduce a new auxiliary differential equation (ADE) collocation radial basis function meshless method (RBF) that utilizes the implicit Cranck-Nicolson (CN) scheme to investigate the propagation of electromagnetic waves in a generally dispersive medium. The suggested method includes an ADE method that uses a difference equation to figure out how the electric field intensity and vector of electric displacement behave in a lossy medium with complex permittivity. The suggested method only applies the CN scheme to Faraday's law, significantly reducing the required memory and processing time. This leads to solving the second-order wave equation with an additional auxiliary variable in the time domain. A two-dimensional cavity loaded with a variety of dispersive mediums is used as an example to validate the accuracy and efficiency of the proposed ADE-CN-RBF method. In this study, the outcomes from the suggested method are more accurate and faster at simulating dispersive media than the traditional ADE-CN-FDTD method.