An Efficient Numerical Approach for Evaluating Sommerfeld Integrals Arising in the Construction of Green's Functions for Layered Media


IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol.7, pp.328-335, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7
  • Publication Date: 2022
  • Doi Number: 10.1109/jmmct.2022.3221835
  • Journal Name: IEEE Journal on Multiscale and Multiphysics Computational Techniques
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.328-335
  • Keywords: Spectral analysis, Method of moments, Green's function methods, Silicon, Integral equations, Interpolation, Standards, Computational electromagnetics (CEM), dyadic Green's function (GF), method of moments (MOM), mixed potential integral equation (MPIE), planar multilayered media, Prony's method, Sommerfeld integral (SI), ELECTROMAGNETIC SCATTERING, ARBITRARY SHAPE, DERIVATION, RADIATION, SURFACES
  • Middle East Technical University Affiliated: Yes


IEEEThis paper presents an efficient approach for evaluating the Sommerfeld integrals in the spectral domain, whose integrands typically show an oscillatory and slowly decaying behavior at high frequencies, e.g., in the millimeter wave regime. It is well known that these integrals arise in the representations of the dyadic Green's functions of layered media and efficient computation of these Green's functions is key to rapid CEM modeling of patch antennas and printed circuits designed for 5G applications in the millimeter wave range. The underlying concept of the approach proposed herein is to partition the spectral domain representation of a Green's function into multiple domains and to represent the envelope of the integrand in each domain with a few exponentials such that the integrals in these domains can be evaluated analytically very efficiently and accurately in a numerically stable manner. Additionally, a new interpolation strategy is proposed in this work to decrease the matrix fill time in the MoM (Method of Moments) solution of the integral equations whose kernels contain Green's functions mentioned above. The performance enhancement realized by using the proposed approaches is demonstrated through several illustrative examples.