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A direct domain-decomposition-based time-domain finite-element method of linear complexity is developed to overcome the challenge of simulating a wide range of geometrical scales present in an integrated circuit (IC) system. Via a set of orthogonal prism vector basis functions, we decompose the entire 3-D system of an IC problem into 2-D subsystems and then into 1-D subsystems with negligible computational cost. We then further decompose each 1-D subsystem into two domains, one with conductors and the other one with dielectrics. A direct solution without any iteration is proposed to solve the resulting system in linear complexity. Furthermore, the method allows for the use of different meshes in different domains. Numerical simulations of ICs and package problems have demonstrated the accuracy, linear complexity, and meshing flexibility of the proposed method.