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Full-chip power grid analysis is time consuming. Several techniques have been proposed to tackle the problem but typically they deal with the power grid as a whole or partition at unnatural boundaries. Using a locality effect under flip-chip packaging, we propose a natural partitioning approach based on overlapping power grid "shells". The technique makes more efficient any previous simulation techniques that are polynomial in grid size. It is also parallelizable and therefore extremely fast. Using complete partitions gives no loss of accuracy compared to a full matrix solution, while lesser partitions are conservative for droop and current. Results on a recent Pentium® microprocessor design show excellent speed and accuracy.