Fast Iterative Solution Algorithms in the Frequency-Domain Layered Finite Element Method for Analyzing Integrated Circuits

摘要

Fast algorithms are developed in this work for solving the system matrix resulting from a frequency-domain layered finite element based analysis of integrated circuits. The frequency-domain layered finite element method represents a 3-D layered system by a 2-D layered system, and further by a single-layered one. The reduced system matrix is generally denser than the original sparse matrix. In this paper, we show that 1) the dense matrix–vector multiplication can be performed in linear complexity; in addition, the reduction cost can be bypassed, 2) an effective preconditioner can be developed to converge the iterative solution of the reduced system matrix in a small number of iterations, and 3) the preconditioner can be solved in linear complexity. As a result, the reduced system matrix can be solved efficiently. The algorithms are rigorous without making any approximation. They apply to any arbitrarily-shaped multilayer structure. Numerical results demonstrated the accuracy, effectiveness, and efficiency of the proposed algorithms in analyzing on-chip circuits.