An Efficient Algorithm for the Numerical Evaluation of Boundary Integral Equations

Abstract

The usual approach to the solution of boundary integral equations is to represent the unknown vector by a piecewise constant, linear, or quadratic function over the given mesh subdivision. These representations have the advantages of consistency, ability to integrate the equations for the given functional approximations, and, in general, improved accuracy as the degree of approximation is increased. While adequate for many problems, special requirements arise for certain nonlinear problems, e.g., plasticity, where the integral equations must be solved for each load increment. In the present paper a special numerical algorithm is outlined in which the unknown vector is represented as a combination of a Fourier series and piecewise linear function. The piecewise linear function is used only in high gradient regions of the unknown vector thus permitting an excellent representation with relatively few Fourier terms. The algorithm is compared with a linear representation alone for two problems which show the effects of multiple connectivity, sharp corners and discontinuous loading. For comparable accuracy both problems show a significant improvement in computer time required.