Interpolatory Nonlinear Model Order Reduction and its Application in Circuit Simulation

This thesis presents a new approach to construct parametrized reduced-order models for nonlinear circuits. The reduced model is obtained such that it matches the variations in the DC operating point of the original full circuit in response to variations in several of its key design parameters. The new approach leverages the discrete empirical interpolation approach developed for model reduction in other domains and enables its efficient application to the problem of DC operating point in nonlinear circuits. Utilizing the idea of rooted trees, the proposed approach constructs orthogonal bases that are used in projecting the full equations of the large original nonlinear circuit onto a reduced system of nonlinear equations in a space with a much smaller dimension. The variations in the DC operating point of the full circuit are then obtained by solving the reduced system of equations, yielding significant computational savings.