  This paper introduces an efficient approach for solving the Electric Field
Integral Equation (EFIE) with high-order accuracy by explicitly enforcing the
continuity of the impressed current densities across boundaries of the surface
patch discretization. The integral operator involved is discretized via a
Nystr\"om-collocation approach based on Chebyshev polynomial expansion within
each patch and a closed quadrature rule is utilized such that the
discretization points inside one patch coincide with those inside another patch
on the shared boundary of those two patches. The continuity enforcement is
achieved by constructing a mapping from those coninciding points to a vector
containing unique discretization points used in the GMRES iterative solver. The
proposed approach is applied to the scattering of several different geometries
including a sphere, a cube, a NURBS model imported from CAD software, and a
dipole structure and results are compared with the Magnetic Field Integral
Equation (MFIE) and the EFIE without enforcing continuity to illustrate the
effectiveness of the approach.
