Improved Quadrature Formula for a Single-Layer Potential

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Abstract

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.

About the authors

P. A. Krutitskii

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Email: biem@mail.ru
125047, Moscow, Russia

I. O. Reznichenko

Faculty of Physics, Lomonosov Moscow State University

Author for correspondence.
Email: io.reznichenko@physics.msu.ru
119991, Moscow, Russia

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