The boundary element method for nonlinear problems

In this paper a boundary-only boundary element method (BEM) is developed for solving nonlinear problems. The presented method is based on the analog equation method (AEM). According Co this method the nonlinear governing equation is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. The solution of the substitute equation is obtained as a sum of the homogeneous solution and a particular one of the nonhomogeneous. The nonhomogeneous term, which is an unknown fictitious domain source distribution, is approximated by a truncated series of radial base functions. Then, using BEM the field function and its derivatives involved in the governing equation are expressed in terms of the unknown series coefficients, which are established by collocating the equation at discrete points in the interior of the domain. Thus, the presented method becomes a boundary only method in the sense that only boundary discretization is required. The additional collocation points inside the domain do not spoil the purr BEM character of the method. Numerical results for certain classical nonlinear problems are presented, which validate the effectiveness and the accuracy of the proposed method. (C) 1999 Elsevier Science Ltd. All rights reserved.