A Novel Strategy for Eliminating the Boundary Layer Effect in the Regularized Integral Identity in PIES for 2D Potential Problem

The paper presents a new strategy for improving the accuracy of solutions near the boundary in the integral identity associated with the parametric integral equation system (PIES) for two-dimensional (2D) potential problems. A significant reduction in accuracy in the zone close to the boundary, also known as the boundary layer effect, is directly associated with the nearly singular properties of kernels present in the integral identity. The paper shows that these singularities can be efficiently eliminated by regularizing the integral identity with the help of the so-called regularizing function with appropriate coefficients. The analyzed examples demonstrate a significant improvement in accuracy, where all integrals of the regularized integral identity are accurately calculated using low-order standard Gauss–Legendre quadrature. The proposed regularization algorithm is independent of the actual boundary shape, its representation and assumed boundary conditions.