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

被引:3
作者
Sheng, Feng [1 ]
Gan, Houle [1 ]
Jiao, Dan [1 ]
机构
[1] Purdue Univ, Sch Elect & Comp Engn, W Lafayette, IN 47907 USA
来源
IEEE TRANSACTIONS ON ADVANCED PACKAGING | 2010年 / 33卷 / 02期
基金
美国国家科学基金会;
关键词
Electromagnetic modeling; finite element method; frequency domain; iterative solver; on chip; preconditioner;
D O I
10.1109/TADVP.2009.2029561
中图分类号
T [工业技术];
学科分类号
08 ;
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.
引用
收藏
页码:524 / 533
页数:10
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