Dense Matrix Factorization of Linear Complexity for Impedance Extraction of Large-Scale 3-D Integrated Circuits

A fast LU factorization of linear complexity is developed to directly solve a dense system of linear equations for the interconnect extraction of any arbitrary shaped 3-D structure embedded in inhomogeneous materials. The proposed solver successfully factorizes dense matrices that involve more than one million unknowns in fast CPU run time and modest memory consumption. Comparisons with state-of-the-art integral-equation-based interconnect extraction tools have demonstrated its clear advantages.