A Recursive Approach for Efficient Computation of The Green’s Function of Multilayer Media with Arbitrarily Shaped Boundaries

Gürbüz T. U., Aslanyürek B.

The Tenth International Conference on Computational Mathematics and Engineering Sciences (CMES-2026), İstanbul, Türkiye, 24 - 26 Nisan 2026, ss.93, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.93
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

We present an efficient computational approach for evaluating the Green’s function of
multilayer media with arbitrarily shaped interfaces. Such Green’s functions play a fundamental
role in a wide range of electromagnetic problems, including inverse scattering, wave
propagation analysis, and the formulation of integral-equation-based solution methods. The
considered configuration consists of multiple homogeneous, isotropic, and nonmagnetic layers
separated by boundaries of arbitrary shape. In this setting, the Green’s function is represented
using an eigenfunction-expansion formulation tailored for noncircular geometries. Imposing
the continuity conditions at the interfaces leads to a large linear system with an almost blockdiagonal
structure, whose direct solution becomes computationally expensive as the number of
layers. To address this challenge, we develop a recursive solution strategy based on a Thomasalgorithm-
like recursive elimination. The proposed method systematically eliminates the
unknown expansion coefficients layer by layer, starting from the innermost region and
proceeding outward. This yields a sequence of recursive relations that allow the efficient
computation of the Green’s-function coefficients without explicitly solving the global system.
The resulting algorithm significantly reduces both computational time and memory
requirements while preserving accuracy. Owing to its efficiency and generality, the proposed
formulation provides a practical tool for large-scale simulations and for applications requiring
repeated evaluations of multilayer Green’s functions.