Direct finite-element solver of linear complexity for system-level signal and power integrity co-analysis

In this paper, we develop a fast direct finite-element solver of linear (optimal) complexity for solving large-scale system-level signal and power integrity problems. The proposed direct solver has successfully analyzed an industry product-level full-package problem and correlated with measurements in time domain. The finite-element matrix of over 15.8 million unknowns resulting from the analysis of the package, including both signal lines and power delivery structures, is directly solved in less than 1.6 hours on a single core running at 3 GHz. Comparisons with the finite element methods that employ the most advanced direct sparse solvers have demonstrated the clear advantages of the proposed high-capacity linear-complexity direct solver.