A Linear-Complexity Finite-Element-Based Eigenvalue Solver for Efficient Analysis of 3-D On-Chip Integrated Circuits

This letter presents a linear-complexity finite-element-based eigenvalue solver for efficient analysis of 3-D on-chip integrated circuits. In this solver, from the original 3-D quadratic eigenvalue problem governing the on-chip circuits, we formulate a new generalized eigenvalue problem to efficiently compute the eigenvalues and eigenvectors of physical interest. We also develop an efficient linear-complexity solution for the matrix equation involved in the solution of the generalized eigenvalue problem. Numerical results demonstrate the accuracy and efficiency of the proposed eigenvalue solver.