Quadrature Formula for the Simple Layer Potential

Resumo

A quadrature formula for the simple layer potential with smooth density specified on a closed or open surface is derived. The formula uniformly approximates the potential near the surface and inherits its continuity as the observation point tends to the surface from the interior of the domain; this has been confirmed by numerical tests. The proposed quadrature formula is much more accurate in calculating the potential near the surface than the standard quadrature formulas, a fact that has also been confirmed by numerical tests.