ИСТИНА

The double layer potential is used in the numerical solution of boundary value problems for the Laplace and Helmholtz equations. With the help of potentials, boundary value problems can be reduced to integral equations, which are then solved numerically. For the numerical solution of integral equations, it is necessary to have quadrature formulas that calculate with good accuracy the direct values of the potentials on the surface, where the potential density is given. Engineering calculations use standard quadrature formulas for the potentials, but their accuracy is poor. An improved quadrature formula for the direct value of the simple layer potential and for the direct value of the normal derivative of the simple layer potential were proposed by the authors before. In this paper, an improved quadrature formula is derived for the direct value of the double layer potential. The improved formula gives significantly higher accuracy than the standard one, which is confirmed by numerical tests. Testing the improved and standard quadrature formulas was carried out in the case when the surface is a sphere of unit radius. The calculation results show that the calculation error using the improved quadrature formula is several times less than the calculation error using the standard quadrature formula. Thus, the improved quadrature formula provides a much higher accuracy in calculating the direct value of the double layer potential. The improved quadrature formula can find application in the numerical solution of boundary integral equations arising in the process of solving boundary value problems for the Laplace and Helmholtz equations by the method of potentials.