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A systematic and efficient algorithm is presented for incorporating multiport lumped networks in terms of admittance matrices into a hybrid field-circuit solver based on the extended time-domain finite-element method. The Laplace-domain admittance matrices are cast into the time-domain stepping equations for port voltages and currents to form a lumped-network subsystem, which is then interfaced with the finite-element and circuit subsystems through shared ports. While the port voltages of the lumped-network subsystem are determined by the finite-element and circuit subsystems, its port currents are treated as external current excitations for the finite-element and circuit subsystems. All the lumped-network port variables are then eliminated from the final expressions to form a global system for only the finite-element and circuit unknowns. The proposed algorithm further extends the capability of the existing field-circuit solver to model more complex and mixed-scale hybrid circuits, and the algorithm is validated and demonstrated through numerical examples.