Numerical integration schemes for Petrov–Galerkin infinite BEM

The present article discusses the numerical approximation of hypersingular integral equations arising from Neumann two-dimensional elliptic problems defined over unbounded domains with unbounded boundaries by using a Petrov–Galerkin infinite boundary element method as discretization technique. An analysis of the singularities, arising during the double integration process needed for the generation of the stiffness matrix elements related to the infinite mesh elements, is carried out and efficient quadrature schemes are proposed. Several numerical results, involving linear elasticity and potential problems defined over various unbounded domains are presented.