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In this paper, we develop an almost embarrassingly parallel solution to an electromagnetic solver of linear complexity for overcoming the grand challenge of performing electromagnetically accurate co-simulation of die-package interaction. In this solution, through suitable basis functions and linear algebraic techniques, we directly and rigorously decompose the system matrix in a 3-D space to multiple matrices of 1-D sizes with negligible computational overhead. Each 1-D matrix is made tridiagonal and, hence, can be solved readily in linear complexity. We then achieve an almost embarrassingly parallel implementation of the fast electromagnetic solver with a low communication-to-computation ratio. Numerical experiments on a large-scale combined die-package system, involving more than 3.5 billion unknowns, have demonstrated superior performance of the proposed parallel transient simulator for simulating large-scale integrated circuits and package problems. In addition, the proposed solver is applicable to any arbitrarily shaped multilayer structure embedded in inhomogeneous materials.