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Ewald summation technique has been proven to be a highly efficient method for rapid calculation of the potential Green's functions in rectangular cavities. It is known that in addition to potential Green's functions, curl of the vector potential Green's function is also needed when applying the mixed potential integral equation method to dielectric objects. In this paper the Ewald sum technique is applied for rapid calculation of these components of the dyadic Green's functions. Several numerical implementation issues including the extraction of singularity when using the Ewald summation method ate also addressed for the first time, leading to further enhancement in computational speed accuracy, and numerical stability.