A rectangle rule for the computation of hypersingular integral

The composite rectangle rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/(x - s)2 is discussed. For the case of singular point coinciding with the mesh point, a new quadrature rule which is based on the classical finite-part definition is presented. A kind of the hypersingular integral equation is solved by collocation methods and the maximal error estimation is given. Some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.