with Y representing boundary conditions and inhomogeneities, X representing the field of interest, and G the integral operator describing how Y is given from X based on the physics of the problem. Next, G is split into G 1 + G 2 , where G 1 is invertible and contains all the singularities of G and G 2 is regular. After splitting the operator and multiplying by the inverse of G 1 , the equation becomes