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Title: Complex-plane generalization of scalar Levin transforms: A robust, rapidly convergent method to compute potentials and fields in multi-layered media

We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the method of weighted averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier–Hankel (F–H) integral transforms. This “complex-plane” MWA, effected via a linear-path detour in the complex plane, results in rapid, absolute convergence of field and potential solutions in multi-layered environments regardless of the source-observer geometry and anisotropy/loss of the media present. In this work, we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra. Subsequently, we (1) exhibit the foundational relations behind the complex-plane extension to a general Levin-type sequence convergence accelerator, (2) specialize this analysis to one member of the Levin transform family (the MWA), (3) address and circumvent restrictions, arising for two-dimensional integrals associated with wave dynamics problems, through minimal complex-plane detour restrictions and a novel partition of the integration domain, (4) develop and compare two formulations based on standard/real-axis MWA variants, and (5) present validation results and convergence characteristics for one of these two formulations.
Authors:
 [1] ;  [1] ;  [2]
  1. The Ohio State University, Electroscience Laboratory, 1330 Kinnear Road, Columbus, OH 43212 (United States)
  2. Halliburton, Sensor Physics and Technology, 3000 N. Sam Houston Pkwy E, Houston, TX 77032 (United States)
Publication Date:
OSTI Identifier:
22314877
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 269; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ANISOTROPY; COMPARATIVE EVALUATIONS; CONVERGENCE; FOURIER TRANSFORMATION; GEOMETRY; HANKEL TRANSFORM; INTEGRALS; MATHEMATICAL SOLUTIONS; POTENTIALS; SCALARS; TWO-DIMENSIONAL CALCULATIONS; VALIDATION