Testing of Quadrature Formulas for the Direct Value of the Normal Derivative of a Single-Layer Potential at the Boundary of a Thin Body

• Published in: Computational mathematics and mathematical physics Vol. 64; no. 10; pp. 2167 - 2177
• Main Authors: Krutitskii, P. A., Reznichenko, I. O.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2024; Springer Nature B.V
• Subjects: Boundary value problems; Computational Mathematics and Numerical Analysis; General Numerical Methods; Integrals; Mathematics; Mathematics and Statistics; Numerical integration; Quadratures; Spheres; Thin bodies; thin body; Laplace equation; quadrature formulas; potential theory
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542524701185

Test examples constructed on an explicit solution to the jump problem are used to compare quadrature formulas for the direct value of the normal derivative of a harmonic single-layer potential at the boundary of a thin body. It is established that the error of a quadrature formula based on numerical integration is several times greater than the error of an improved quadrature formula based on the analytical calculation of integrals. Numerical tests show that the improved quadrature formula provides acceptable numerical accuracy even in the case when the body thickness is significantly smaller than the integration step, so the required numerical accuracy can be achieved at a lower cost. The results can be used to numerically solve boundary value problems in thin bodies and layered media by applying the potential method.