A hierarchical domain decomposition method for rigorous conductor modeling of signal integrity in multi-scale integrated circuits

We present a hierarchical multi-solver domain decomposition method to accurately analyzing the signal integrity problems in multi-scale integrated circuits. Particularly, we discuss in detail a 3-D full wave method to model the conductor loss due to finite conductivities in metals. The proposed multi-solver non-conformal domain decomposition method follows a hierarchical domain partitioning strategy and the original problem is decomposed into non-overlapping subregions. A finite element domain decomposition method is adopted for the dielectric subregion with complex geometries and non-uniform material properties. While for the conductor subregion, a surface integral equation domain decomposition method is applied. To further improve the convergence in the DDM iterations, optimized transmission conditions are introduced to enforce the field continuities across sub-domain interfaces. Moreover, a hierarchical multi-level fast multiple method is adopted to address the low frequency issues particularly in IC applications. Rigorous numerical experiments validate the potential benefits offered by the proposed method.