Preconditioned Second-Order Multi-Point Passive Model Reduction for Electromagnetic Simulations

A second-order multi-point Krylov subspace projection based model order reduction process for electromagnetic simulations is presented. The electromagnetic setup is converted to a second-order model-susceptance element based equivalent circuit. The state-space representation of this equivalent circuit is suitably reduced through a model order reduction process, where the recursive calculation of the projection matrix is done through a preconditioned iterative method. Issues concerning the passivity of the reduced system are discussed. The single-point and multi-point schemes are validated through numerical examples. The second-order multi-point algorithm for the reduction process is shown to be advantageous in matching response curves exhibiting complex behavior.