Solution of potential problems using combinations of the regular and derivative boundary integral equations (Q751209)

Using combinations of the boundary integral equation (BIE) and the normal derivative of the boundary integral equation (DBIE) two hybrid methods are investigated. In the first method, designated as HBEM1, the BIE is written at collocation nodes along the boundary where Neumann boundary conditions are prescribed, and the DBIE is written at collocation nodes along the boundary where Dirichlet boundary conditions are prescribed. An alternative method is HBEM2, in which the above mentioned conditions are reversed. The HBEM1 yields a system of Fredholm integral equations of the second kind, while the HBEM2 yields a system of Fredholm integral equations of the first kind. Three examples are investigated, and numerical and analytical results are compared and discussed.