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

Time-domain layered finite element reduction recovery (LAFE-RR) method was recently developed for large scale electromagnetic analysis of high-speed ICs. This method is capable of analytically and rigorously reducing the system matrix of a 3D multilayer circuit to that of a single layer one irrespective of the original problem size. In addition, it preserves the sparsity of the original system matrix. In this paper, we propose an efficient algorithm 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 CPU run time and memory consumption. The cost of matrix factorization is negligible. The cost of matrix solution is linear. Numerical and experimental results have demonstrated the accuracy and efficiency of the proposed algorithm.