Detailed Description

Nearly singular integrals for the Laplace kernels.

This file contains the specialised implementations of some nearly singular integrals for the Laplace kernel and its normal derivatives. These include SLP, DLP, DLPt, and HSP kernels.

For planar elements, the method of integration generally relies on a planar transformation that transforms the element to plane parallel with the x-y plane. Then, a semi-analytical integration is performed in polar coordinates. The integration along the radius is evaluated analytically, while the integration with respect to the angle is performed using quadratures. The latter integration is performed by subdividing the planar element into plane triangular domains of integration.

The file also contains the shortcut classes that enable the specialised implementations for different kernels and element types.

Definition in file laplace_2d_nearly_singular_integrals.hpp.