Reduced Order Method for Solving Large-Scale Quadratic Eigenvalue Problems

Quadratic eigenvalue problems are frequently encountered in electromagnetic analysis of lossy dielectrics and conductors. We present a fast method for solving large-scale quadratic eigenvalue problems. The method reduces the order of the original quadratic eigenvalue problem to a small one to solve. The computational cost of the reduction is simply a small number of solutions of an underlying deterministic problem, which are obtained in linear complexity. Applications to electromagnetics-based analysis of large-scale on-chip power grids demonstrate the accuracy and efficiency of the method.