Field of potential in a compound rectangle containing a linear inclusion
A boundary-value problem in the theory of potential for the compound domain composed of two homogeneous rectangles is solved by the Green's function method. One of the rectangles contains a linear inclusion that is perpendicular to the interface, and whose tip contacts the interfacing line. The integrals (potentials) over the segment of the inclusion are utilized in the solution algorithm. The kernels in these potentials are constructed from the entries in the corresponding matrix of Green's type. In addition, the weakly singular integral equation that results from the formulation of the problem is analyzed. Numerical results demonstrate the accuracy and efficiency of the approach.