Title :
A Recovery Algorithm of Linear Complexity in the Time-Domain Layered Finite Element Reduction Recovery (LAFE-RR) Method for Large-Scale Electromagnetic Analysis of High-Speed ICs
Author :
Gan, Houle ; Jiao, Dan
Author_Institution :
Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN
Abstract :
Time-domain layered finite element reduction recovery (LAFE-RR) method was recently developed for large-scale electromagnetic analysis of high-speed integrated circuits (ICs). This method is capable of analytically and rigorously reducing the system matrix of a 3-D multilayer circuit to that of a single-layer one regardless of the original problem size. In addition, the reduced system matrix preserves the sparsity of the original system matrix. In this paper, an efficient algorithm is proposed to recover the volume unknowns in the time-domain LAFE-RR method. This algorithm constitutes a direct solution of the matrix formed by volume unknowns in each layer. This direct solution possesses a linear complexity in both central processing unit (CPU) time and memory consumption. The cost of matrix inversion is negligible. The cost of matrix solution scales linearly with the matrix size. Numerical and experimental results have demonstrated the accuracy and efficiency of the proposed algorithm.
Keywords :
VLSI; computational complexity; finite element analysis; high-speed integrated circuits; matrix algebra; time-domain analysis; 3D multilayer circuit; central processing unit time; high-speed ICs; high-speed integrated circuits; large-scale electromagnetic analysis; linear complexity; matrix inversion; memory consumption; system matrix; time-domain layered finite element reduction recovery method; very large scale integrated circuits; Electromagnetic analysis; finite-element methods; time domain analysis; very large scale integrated circuits;
Journal_Title :
Advanced Packaging, IEEE Transactions on
DOI :
10.1109/TADVP.2008.920648