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 language | English |
|---|---|
| Pages (from-to) | 7908-7917 |
| Number of pages | 10 |
| Journal | IEEE Transactions on Antennas and Propagation |
| Volume | 73 |
| Issue number | 10 |
| DOIs | |
| State | Published - 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