A general algorithm for accurate computation of field variables and its derivatives near the boundary in BEM

A general algorithm was proposed in the paper for the accurate computation of the field variables and its derivatives at domain points near the boundary in attempt to solve the so-called boundary layer effect in the boundary element method. The algorithm is based on the parameter, including modified Gauss-Tschebyscheff quadrature formula with the aid of the approximate distance function introduced, where the parameter is defined as the ratio of the minimum distance of the domain point to the boundary and the length of the boundary element. The algorithm is not only numerically stable because the singular part of the integrand serves as the weight function in the modified Gauss-Tschebyscheff quadrature formula but also independent of the kind of boundary elements. The method can be extended to the three-dimensional case with little modifications. Numerical examples of the potential problem and the elastic problem of plane strain were given by using the cubic and the quadratic boundary elements, respectively, showing the feasibility and the effectiveness of the proposed algorithm. (C) 2001 Elsevier Science Ltd. All rights reserved.