An enhanced BEM approach applied to potential problems: a comparative study

In the present paper, a hybrid analytical/numerical method capable of integrating singular logarithmic functions, as an essential part of the Boundary Element Method (BEM) process, is presented. The proposed scheme provides a more practical approach through the reduction of the computational effort of the analytical method. For this purpose, the singular function is divided into two parts of singular and non-singular. The non-singular part is numerically integrated, while the singular part is analytically integrated and the result of both parts is combined. The capabilities and accuracy of the proposed scheme are investigated through various elemental and potential examples. The results of numerical comparisons indicate the ability of the proposed scheme to reduce the computational effort of the analytical solutions, which develops an appropriate alternative for the simple analytical solution of the potential problems that can be used in practical modeling problems such as heat transfer.