Self-adapting algorithm for evaluation of weakly singular integrals arising in the boundary element method

Numerical integration scheme for singular integrals based on polar coordinates free from angular quasi–singularities

“…As it was previously mentioned, primary angular quasi-singularities are those strong quasi-singularities emerging when the collocation point is near an element edge or vertex. This issue has been treated via h (integration domain subdivision) and/or p (adaptive quadrature rule) refinement [18], and non-linear transformations [13,19,15]. The hand prefinement essentially treat the issue by increasing the number of integration points.…”

“…They suffer from two serious defects which affect their efficiency: dependency on the location of the collocation point and element shape (aspect ratio and skewness). The first defect arises from strong quasisingularities in the angular coordinate, and it can be treated with classical techniques such as h− and/or p− refinement [18] or non-linear transformations [13,19]. The second defect also also arises from quasisingularities appearing when tangent vectors along local coordinates are neither equal nor orthogonal at the collocation point, i.e.…”

Analysis of 3D Elastoplastic Notch and Crack Problems using Boundary Element Method

“…The techniques applied for numerical evaluation of all integrals occurring in the boundary integral equations for elastoplastic material behaviour are described in the report [25]. More details on this topic can be found in the articles [2,10,14,18,19,35].…”

Numerical quadrature over triangles with weak singularities

“…Since (34) implies y = xt(Á), the choices in (35) have the e ect to map the line Á = 0 onto the line y = 0, the line Á = 1 onto the line y = tan( )x and generally lines Á = constant onto radial lines emanating from the origin x = 0; y = 0.…”