Fast iterative solution algorithms for the frequency-domain layered finite-element based analysis of large-scale on-chip interconnect structures

An effective preconditioner P is proposed in this work for solving the surface-unknown-based reduced system matrix in the frequency-domain layered finite element method. This preconditioner is effective because it can converge the iterative solution of the reduced system matrix in a few iterations. It is computationally efficient because P^-1b with b being an arbitrary vector can be obtained in linear complexity in both CPU time and memory consumption. With this preconditioner, the reduced system matrix in the layered finite element method is solved efficiently. The algorithms are rigorous without making any approximation. They apply to any arbitrarily-shaped multilayer structure. Numerical and experimental results demonstrated the accuracy, effectiveness, and efficiency of the proposed fast solution algorithms in analyzing large-scale on-chip interconnects.