Solution of Maxwell’s equations for nonrectangular electromagnetic applications

Abstract

The use of a fourth-order modified Runge–Kutta (MRK) scheme on a transformed coordinate system with Maxwell’s equations for nonrectangular domains and applications is presented. Maxwell’s equations are the governing equations for modeling electromagnetic wave propagation involving scattering, radiating structures, transmission lines, radar, biomedical applications, and nondestructive testing. Because of complex geometries in most problems where the material boundaries are not parallel to the grid axis, the application of finite differencing schemes in physical coordinates becomes nonviable. Therefore, by transforming the arbitrary-shaped structures to a uniform rectangular grid, numerical schemes and boundary conditions can be easily implemented. Numerical results for four cases are presented in this paper. Accuracy of the scheme has been established by comparing numerical results with the exact solution and error distribution plots. In the third case, scattering from the lossless and the lossy square cylindrical dielectric device where the plane wave source is injected using the total-field–scattered-field technique has been investigated. The results are compared with the results obtained from the benchmark finite difference time domain scheme. Lastly, the application of the numerical model to simulate scattering from curved boundaries has been presented in the fourth example.