Efficient Computation of Electromagnetic Waves under Cylindrical Geometries Using Spectral Numerical Mode Matching (SNMM) Method

The numerical mode matching (NMM) method is a widely used semi-analytical approach for modeling the propagation of electromagnetic (EM) waves in orthogonal-plano-cylindrically layered (OPCL) media. In this paper, we present four significant enhancements aimed at augmenting the efficiency, accuracy, and applicability of the NMM method: (1) We introduce the Spectral Element Method (SEM) to efficiently calculate eigenmodes within each horizontally stratified layer with radial variations. The SEM employs Gauss-Lobatto-Legendre polynomials as basis functions to expand the EM field and leverages efficient numerical quadrature for integration. Our study demonstrates that this SEM-based NMM (SNMM) approach offers superior efficiency and accuracy compared to the Finite Element Method (FEM)-based NMM method, while also requiring lower memory resources. (2) Apart from the dipole sources, we expand the capabilities of the SNMM method to simulate EM fields generated by current line sources, broadening its applicability in geophysical exploration. (3) By exploiting field symmetry between two harmonics with opposite mode indices for various excitation scenarios, we achieve a significant reduction in computational time, effectively halving the simulation effort. (4) To enhance the condition of the system matrix and improve result accuracy, we introduce a scale factor that reduces the contrast of elements in the mass matrix. This adjustment ensures better numerical stability and fidelity in our simulations. The numerical examples demonstrate the accuracy and efficiency of the proposed SNMM method.