Matrix computations (3rd ed.)
Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods
Proceedings of the 38th annual Design Automation Conference
A static pattern-independent technique for power grid voltage integrity verification
Proceedings of the 40th annual Design Automation Conference
A geometric approach for early power grid verification using current constraints
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Stochastic Preconditioning for Diagonally Dominant Matrices
SIAM Journal on Scientific Computing
Fast vectorless power grid verification using an approximate inverse technique
Proceedings of the 46th Annual Design Automation Conference
An efficient dual algorithm for vectorless power grid verification under linear current constraints
Proceedings of the 47th Design Automation Conference
Hierarchical analysis of power distribution networks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Power grid analysis using random walks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Vectorless verification of RLC power grids with transient current constraints
Proceedings of the International Conference on Computer-Aided Design
Parallel forward and back substitution for efficient power grid simulation
Proceedings of the International Conference on Computer-Aided Design
Overview of vectorless/early power grid verification
Proceedings of the International Conference on Computer-Aided Design
Constraint abstraction for vectorless power grid verification
Proceedings of the 50th Annual Design Automation Conference
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Vectorless power grid verification is a powerful technique to validate the robustness of the on-chip power distribution network for all possible current waveforms. Formulated and solved as linear programming problems, vectorless power grid verification demands intensive computational power due to the large number of nodes in modern power grids. Previous work showed that the performance bottleneck of this powerful technique is within the sub-problem of power grid analysis, which essentially computes the inverse of the sparse but large power grid matrix. In this paper, we propose a hierarchical matrix inversion algorithm to compute the rows of the inverse efficiently by exploiting the structure of the power grid. The proposed algorithm is integrated with a previous dual algorithm addressing an orthogonal sub-problem for vectorless power grid verification. Results show that the proposed hierarchical algorithm accelerates the matrix inversion significantly, and thus makes the overall vectorless power grid verification efficient.