A multilevel ℌ-matrix-based approximate matrix inversion algorithm for vectorless power grid verification

Vectorless power grid verification technique makes it possible to estimate the worst-case voltage fluctuations of the on-chip power delivery network at the early design stage. For most of the existing vectorless verification algorithms, the sub-problem of linear system solution which computes the inverse of the power grid matrix takes up a large part of the computation time and has become a critical bottleneck of the whole algorithm. In this paper, we propose a new algorithm that combines the ℌ-matrix-based technique and the multilevel method to construct a data-sparse approximate inverse of the power grid matrix. Experimental results have shown that the proposed algorithm can obtain an almost linear complexity both in runtime and memory consumption for efficient vectorless power grid verification.