A deterministic-solution based fast quadratic eigenvalue solver for 3-D finite element analysis

A fast solution to the quadratic eigenvalue problem resulting from the finite element based analysis of general electromagnetic problems with lossy conductors and materials is developed. Given an arbitrary frequency band, the proposed solver is capable of solving a significantly reduced eigenvalue problem of O(k) to find a complete set of the eigenvalues and eigenvectors that are physically important for this frequency band, the number of which is k. The reduced eigenvalue problem is constructed from O(k) solutions to a deterministic problem. Its convergence and accuracy are theoretically proved. The proposed solver is applicable to general 3-D problems where the structures are arbitrary, materials are inhomogeneous, and both dielectrics and conductors can be lossy.