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A time-domain orthogonal finite-element reduction-recovery method is developed to overcome the large problem sizes encountered in the simulation of large-scale integrated-circuit and package problems. In this method, a set of orthogonal prism vector basis functions is developed. Based on this set of bases, an arbitrary 3-D multilayered system such as a combined package and die is reduced to a single-layer system with negligible computational cost. More importantly, the reduced single-layer system is diagonal and, hence, can be solved readily. From the solution of the reduced system, the solution of the other unknowns is recovered in linear complexity. The method entails no theoretical approximation. It applies to any arbitrarily shaped multilayer structure involving inhomogeneous materials or any structure that can be geometrically modeled by triangular prism elements. In addition, it permits nonlinear device modeling and broadband simulation within one run. Numerical and experimental results have demonstrated its accuracy and high capacity in simulating on-chip, package, and die-package interface problems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]