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.

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Cosmology simulations are highly communicationintensive, thus it is critical to exploit topology-aware task mapping techniques for performance optimization. To exploit the architectural properties of multiprocessor clusters (the performance gap between inter-node and intra-node communication as well as the gap between inter-socket and intra-socket communication), we design and develop a hierarchical task mapping scheme for cell-based AMR (Adaptive Mesh Refinement) cosmology simulations, in particular, the ART application. Our scheme consists of two parts: (1) an inter-node mapping to map application processes onto nodes with the objective of minimizing network traffic among nodes and (2) an intra-node mapping within each node to minimize the maximum size of messages transmitted between CPU sockets. Experiments on production supercomputers with 3D torus and fat-tree topologies show that our scheme can significantly reduce application communication cost by up to 50%. More importantly, our scheme is generic and can be extended to many other applications.

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