Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision

Research output: Contribution to journalArticlepeer-review

Abstract

Analytic expressions are developed for integrals over curvilinear domains where the integrands are the product of polynomial bases with natural logarithm kernels whose arguments are polynomial. These integrands occur directly in 2-D electrostatic integral equations and indirectly in 2-D electrodynamic integral equations with singularity extractions. The analytic results are validated in double precision using an arbitrary-precision math library, and near-machine precision accuracy is observed over a wide range of parameter inputs. Limitations of the analytic expressions are also presented.

Original languageEnglish
Pages (from-to)7908-7917
Number of pages10
JournalIEEE Transactions on Antennas and Propagation
Volume73
Issue number10
DOIs
StatePublished - 2025

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Funding

Received 25 June 2024; revised 23 April 2025; accepted 8 June 2025. Date of publication 26 June 2025; date of current version 14 October 2025. This work was supported by the Department of Education’s Graduate Assistance in Areas of National Need (GAANN) Fellowship Program through the University of Kentucky Electrical and Computer Engineering Department. (Corresponding author: Jordon N. Blackburn.) The authors are with the Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2025.3581670

Funders
U.S. Department of Education Institute of Education Sciences
University of Kentucky

    Keywords

    • Electrodynamics
    • electrostatics
    • higher-order numerical methods
    • logarithmic kernels
    • singular integrals

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering

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