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Full-wave solutions of Maxwell's equations break down at low frequencies. Existing methods for solving this problem either are inaccurate or incur additional computational cost. In this paper, a fast full-wave finite-element-based solution is developed to eliminate the low-frequency breakdown problem in a reduced system of order one. It is applicable to general 3-D problems involving ideal conductors as well as nonideal conductors immersed in inhomogeneous, lossless, lossy, and dispersive materials. The proposed method retains the rigor of a theoretically rigorous full-wave solution recently developed for solving the low-frequency breakdown problem, while eliminating the need for an eigenvalue solution. Instead of introducing additional computational cost to fix the low-frequency breakdown problem, the proposed method significantly speeds up the low-frequency computation.