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Abstract: The surface-volume-surface electric field integral equation (SVS-EFIE) can lead to complex equations, laborious implementation, and unacceptable computational complexity in the method of moments (MoM). Therefore, a general matrix equation (GME) is proposed for electromagnetic scattering from arbitrary metal-dielectric composite objects, and its enhanced solution is presented in this paper. In the previous work, the MoM solution formulation of the SVS-EFIE considering only three-region metal-dielectric composite scatters was presented, and the two-stage process resulted in two integral operators in the SVS-EFIE, which was arduous to implement and incapable of reducing computational complexity. To address these difficulties, the GME, which is versatile for homogeneous objects and composite objects consisting of more than three sub-regions, is proposed for the first time. Accelerated solving policies are proposed for the GME based on the coupling degree concerning the spacing between sub-regions, and the coupling degree standard can be adaptively set to balance the accuracy and efficiency. In this paper, the reformed addition theorem is applied for the strong coupling case, and the iterative method is presented for the weak coupling case. In addition, parallelism can be easily applied in the enhanced solution.