Improved Quadrature Formula for a Single-Layer Potential

An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform approximation of the potential near the surface and preserves the continuity of the potential as the observation point tends to the surface fr...

Full description

Saved in:
Bibliographic Details
Published inComputational mathematics and mathematical physics Vol. 63; no. 2; pp. 187 - 201
Main Authors Krutitskii, P. A., Reznichenko, I. O.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.02.2023
Springer Nature B.V
Subjects
Accuracy
Boundary value problems
Computational Mathematics and Numerical Analysis
General Numerical Methods
Helmholtz equations
Integral equations
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Quadratures
uniform approximation
single-layer potential
quadrature formula
Online AccessGet full text
ISSN0965-5425
1555-6662
DOI10.1134/S0965542523020100

Cover

More Information
Summary:An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform approximation of the potential near the surface and preserves the continuity of the potential as the observation point tends to the surface from inside the domain. These properties are confirmed by numerical tests. For the potential computed near the surface, the present quadrature formula yields higher accuracy than previously known quadrature rules, which is also confirmed by numerical tests. Additionally, a quadrature formula for the direct value of the single-layer potential on the surface is derived. Numerical tests conducted with this formula confirm its efficiency and accuracy.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523020100