TESTING OF QUADRATURE FORMULAS FOR THE DIRECT VALUE OF THE NORMAL DERIVATIVE OF A SINGLE-LAYER POTENTIAL AT THE BOUNDARY OF A THIN BODY

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Abstract

Using test examples constructed on the basis of an explicit solution of the jump problem, a comparison of quadrature formulas for the direct value of the normal derivative of the harmonic single-layer potential on the boundary of a thin body is carried out. It is established that the error of calculations using the quadrature formula based on numerical integration is several times greater than the error of calculations using the improved quadrature formula based on the analytical calculation of integrals. As numerical tests have shown, the improved quadrature formula provides acceptable calculation accuracy even when the thickness of the body is significantly smaller than the integration step, which makes it possible to achieve the required calculation accuracy at a lower cost. The obtained results can be used for numerical solution of boundary value problems in thin bodies and in layered media by the potential method.

About the authors

P. A Krutitskii

M.V. Keldysh IAM, RAS

Email: biem@mail.ru
Moscow

I. O Reznichenko

M.V. Keldysh IAM, RAS

Email: io.reznichenko@physics.msu.ru
Moscow

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