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This paper presents an efficient time-domain method for computing the propagation of electromagnetic waves in microwave structures. The procedure uses high-order vector bases to achieve high-order accuracy in space, Newmark's method to provide unconditional stability in time, and the transfinite-element method to truncate the waveguide ports. The resulting system matrix is real, symmetric, positive-definite, and can be solved by using the highly efficient multilevel preconditioned conjugate gradient algorithm. Since the method allows large time steps and nonuniform grids, the computational complexity for problems with irregular geometries is superior to that of the finite-difference time-domain method.