Title :
Fast Iterative Solution Algorithms in the Frequency-Domain Layered Finite Element Method for Analyzing Integrated Circuits
Author :
Sheng, Feng ; Gan, Houle ; Jiao, Dan
Author_Institution :
Sch. of Electr. & Comput. Eng., Purdue Univ. West Lafayette, West Lafayette, IN, USA
fDate :
5/1/2010 12:00:00 AM
Abstract :
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.
Keywords :
finite element analysis; frequency-domain analysis; integrated circuit design; iterative methods; network analysis; sparse matrices; frequency-domain layered finite element method; integrated circuits analysis; iterative solution algorithms; on-chip circuits; sparse matrix; system matrix; Electromagnetic modeling; finite element method; frequency domain; iterative solver; on chip; preconditioner;
Journal_Title :
Advanced Packaging, IEEE Transactions on
DOI :
10.1109/TADVP.2009.2029561