The calculation of nearly singular integrals about points close to boundary in boundary integral equation

This paper gives a general algorithm to deal with the difficult problem of calculating the quantities at interior points very close to the boundary by the boundary element method(BEM). In the algorithm, which is applied to solving two dimensional problems, the least distance from the source point to near boundary element is transformed out of the integral representations of the element with an integration by parts, so that the nearly strongly singular and nearly hypersingular integrals are successfully computed.The algorithin can also be used to analyze the plates and shells problems with the BEM.Especially,it is more efficient for solving the nearly singular integrals when the supersingular boundary integral equation(BIE) are regularized to the strongly singular BIE.