A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems

摘要

Meshless method for solving boundary value problems have been extensively popularized in recent literature owing to their flexibility in engineering applications, especially for problems with discontinuities, and because of he high accuracy of the computed results. A method for solving linear and non-linear boundary value problems, based on the local boundary integral equation method and the mopping lest squares (MLS) approximation, is discussed in the present article. In the present article, the implementation of the LBIE formulation for linear and non-linear problems with the linear part of the differential operator being the Helmohotz type, is developed. For non-linear problems, the total formulation and rate formulation are developed for the implementation of the presently proposed method. The present method is a true meshless one, as it does not need domain and boundary elements to deal with the volume and boundary integrals, for linear as well as non-linear problems.