Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision

Jordon N. Blackburn; John C. Young

doi:10.1109/TAP.2025.3581670

Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision

Jordon N. Blackburn
, John C. Young

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	7908-7917
Número de páginas	10
Publicación	IEEE Transactions on Antennas and Propagation
Volumen	73
N.º	10
DOI	https://doi.org/10.1109/TAP.2025.3581670
Estado	Published - 2025

Nota bibliográfica

Publisher Copyright:
© 1963-2012 IEEE.

Financiación

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.

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

ASJC Scopus subject areas

Electrical and Electronic Engineering

Acceder al documento

10.1109/TAP.2025.3581670

Otros archivos y enlaces

Citar esto

@article{323e575e0aee47dab5ce2e18cae859a0,

title = "Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision",

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.",

keywords = "Electrodynamics, electrostatics, higher-order numerical methods, logarithmic kernels, singular integrals",

author = "Blackburn, \{Jordon N.\} and Young, \{John C.\}",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2025",

doi = "10.1109/TAP.2025.3581670",

language = "English",

volume = "73",

pages = "7908--7917",

number = "10",

}

TY - JOUR

T1 - Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision

AU - Blackburn, Jordon N.

AU - Young, John C.

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Electrodynamics

KW - electrostatics

KW - higher-order numerical methods

KW - logarithmic kernels

KW - singular integrals

UR - https://www.scopus.com/pages/publications/105009430492

UR - https://www.scopus.com/pages/publications/105009430492#tab=citedBy

U2 - 10.1109/TAP.2025.3581670

DO - 10.1109/TAP.2025.3581670

M3 - Article

AN - SCOPUS:105009430492

SN - 0018-926X

VL - 73

SP - 7908

EP - 7917

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 10

ER -

Analytic Logarithm Integrals on Curved Contours With Near-Machine Precision

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto