Study Of The Singularity Integrals And The Boundary Layer Effect In Bem

The boundary element method (BEM) is a kind of important calculation as the finite element method (FEM).It has many advantages as the dimensionality of the problems is reduced by one. which have the advantage of reducing the amount of calculation and its error only comes from the discretization of the boundary , etc; it offers the higher accuracy and the tremendous value in the potential problems , the elasticity problems , the hydromechanics , the electromagnetic field , especially the rock engineering and in industrial application. The study on BEM has been a challenging topic for the scientists, the engineers and technicians.In this article, the problems in the BEM are introduced briefly after the principle and methods of the numerical methods are given.Second, the theoretical basis of the BEM in mathematics is introduced in a systematic way such as Green formula, the basic solution, the boundary unit, etc; The BEM of the 2D potential prombles and elasticity problems is presented in detail.Third, the method to solve the singularity is proposed by using intergolation methods on base of the study on the singularity integrals, and the formulation of the solving singularity integrals is present in the theory, a numerical example shows its validity.Forth, The new method to solve the boundary layer effect on 2D and 3D is given by using intergolation method on base of the study on the boundary layer effect, the formula how to locate the nodes of the intergolation function is given, the numerical examples show that the method is correct, and not only are simple but also have higher accuracy.In addition, some studying directions of BEM also are showed in the dissertation.