A new domain decomposition scheme based on equivalence principle algorithm (EPA) is proposed for analyzing electromagnetic scattering from connected structures. The EPA transforms the unknown of inside scatterers to the unknown on the equivalence surfaces which enclose the scatterers. In this paper, the EPA combined with source reconstruction method is introduced to deal with the connected problems. This scheme can avoid the current singularity and keep the good convergence of EPA equations. Furthermore, the gird-robust higher order vector basis (GRHOVB) is used on the equivalence surface to reduce the number of unknowns and improve the accuracy. Numerical results demonstrate the accuracy and efficiency of the proposed method.