An efficient algorithm is introduced to enhance the convergence of dyadic Green's functions (DGF) in a layered spherical media where asymptotic expressions have been developed. The formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media Green's function using the addition theorem of spherical Hankel functions. Substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original DGF. The subtracted components are then added to the solution using the homogenous media Green's function format. \u
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