A meshless regularized local boundary integral equation method and the selection of weight function and geometrical parameters

Abstract

The local boundary integral equation (LBIE) method is a pure meshless integral method proposed by Atluri and co-workers. Since the fundamental solutions are used as the test functions, the sub-domain can be very small and the LBIE method is a promising method for solving problems of elasticity with nonhomogeneous material properties. In this paper, the subtraction technique is introduced to remove the strong singularity that results in a regularized local boundary integral equation (RLBIE) method. The formula is rather straightforward and more accurate than other treatment techniques. Compared with other meshless methods, more geometrical parameters need to be assigned in the method. If the parameters change a little bit, the solutions obtained from the method may fluctuate quickly and uncertainly. Therefore the effects of weight function, support domain, sub-domain, and monomial basis are investigated and how to select the parameters is discussed. The appropriate parameters can be determined and the meshless RLBIE method is an accurate and robust method.