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Considerable improvements can be obtained in battery performance for hybrid electric vehicles (HEVs) by employing an electrochemistry-transport model based on a multi-physics modeling framework and ultrafast numerical algorithms. One important advantage of this approach over the lumped equivalent circuit (or look-up table) approach is the ability of the former to adapt to changes in design and control. In this work, we present mathematical and numerical details of our approach, and demonstrate the robustness of this battery model in simulation of short-pulse charge/discharge characteristic of HEV driving cycles under room and low temperatures.