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We propose the complex-plane generalization of a powerful algebraic sequenceacceleration algorithm, the Method of Weighted Averages (MWA), to guaranteeexponential-cum-algebraic convergence of Fourier and Fourier-Hankel (F-H)integral transforms. This "complex-plane" MWA, effected via a linear-pathdetour in the complex plane, results in rapid, absolute convergence offield/potential solutions in multi-layered environments regardless of thesource-observer geometry and anisotropy/loss of the media present. In thiswork, we first introduce a new integration path used to evaluate the fieldcontribution arising from the radiation spectra. Subsequently, we (1) exhibitthe foundational relations behind the complex-plane extension to a generalLevin-type sequence convergence accelerator, (2) specialize this analysis toone member of the Levin transform family (the MWA), (3) address and circumventrestrictions, arising for two-dimensional integrals associated with wavedynamics problems, through minimal complex-plane detour restrictions and anovel partition of the integration domain, (4) develop and compare twoformulations based on standard/real-axis MWA variants, and (5) presentvalidation results and convergence characteristics for one of these twoformulations.

Complex-Plane Generalization of Scalar Levin Transforms: A Robust, Rapidly Convergent Method to Compute Potentials and Fields in Multi-Layered Media