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
Early-stage power grid analysis for uncertain working modes
Proceedings of the 2004 international symposium on Physical design
Handling inductance in early power grid verification
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
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
Power grid analysis using random walks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
More realistic power grid verification based on hierarchical current and power constraints
Proceedings of the 2011 international symposium on Physical design
Power grid verification using node and branch dominance
Proceedings of the 48th Design Automation Conference
Vectorless verification of RLC power grids with transient current constraints
Proceedings of the International Conference on Computer-Aided Design
A hierarchical matrix inversion algorithm for vectorless power grid verification
Proceedings of the International Conference on Computer-Aided Design
Scalable vectorless power grid current integrity verification
Proceedings of the 50th Annual Design Automation Conference
Constraint abstraction for vectorless power grid verification
Proceedings of the 50th Annual Design Automation Conference
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Vectorless power grid verification makes it possible to evaluate worst-case voltage drops without enumerating possible current waveforms. Under linear current constraints, the vectorless power grid verification problem can be formulated and solved as a linear programming (LP) problem. However, previous approaches suffer from long runtime due to the large problem size. In this paper, we design the DualVD algorithm that efficiently computes the worst-case voltage drops in an RC power grid. Our algorithm combines a novel dual approach to solve the LP problem, and a preconditioned conjugate gradient power grid analyzer. Our dual approach exploits the structure of the problem to simplify its dual problem into a convex problem, which is then solved by the cutting-plane method. Experimental results show that our algorithm is extremely efficient -- it takes less than an hour to complete the verification of a power grid with more than 50K nodes and it takes less than 1 second to verify one node in a power grid with more than 500K nodes.