Calculation of domain integrals of two dimensional boundary element method

In this paper, a new method is applied to deal with domain integrals of boundary element method (BEM). In fact we focus to convert the domain integrals into boundary integrals for non-homogenous Laplace, Helmholtz and advection diffusion equations in two dimensional BEM. The transformation presented in this paper is based on divergence theorem. In addition, we prove the efficiency of method mathematically when the domain integrals are weakly singular. Numerical results are presented to verify the validity of this method for different geometries. Numerical implementation is done for the constant BEM, which can be implemented easily. To verify the new scheme, some test problems have been designed at end of the paper. The numerical results generally show that the new scheme has good accuracy with regards to other popular schemes.