A Numerical Method for Low-Frequency Electromagnetic Fields in a Nonhomogeneous Medium in the Case of H-Polarization

Abstract

We consider finite-difference modeling of the electromagnetic field in a nonhomogeneous medium in the case of H-polarization. At the interior grid points, the finite-difference approximation binds five neighboring values of the grid functions, which correspond to the five diagonals of the linear algebraic system matrix. The matrix is banded. The linear algebraic system is solved by decomposing the matrix into a product of an upper-triangular matrix and a lower-triangular matrix. The algorithm is implemented for complex matrices using double-precision arithmetic. We show how to use the grid function values obtained by solving the linear algebraic system to find the magnetic field at the corner point of the conductivity discontinuity boundary. Calculation of the field at the corner point of the conductivity discontinuity boundary is an independent difficult problem of mathematical modeling of electromagnetic fields in nonhomogeneous media that deserves special attention. An equation is obtained for the field value at the corner point of the boundary. The numerical results obtained for the electromagnetic field in a complex nonhomogeneous medium confirm the validity of this equation.