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Despite temperature rise being a first-order design constraint, traditionalthermal estimation techniques have severe limitations in modeling criticalaspects affecting the temperature in modern-day chips. Existing thermalmodeling techniques often ignore the effects of parameter variation, which canlead to significant errors. Such methods also ignore the dependence ofconductivity on temperature and its variation. Leakage power is alsoincorporated inadequately by state-of-the-art techniques. Thermal modeling is aprocess that has to be repeated at least thousands of times in the designcycle, and hence speed is of utmost importance.  To overcome these limitations, we propose VarSim, an ultrafast thermalsimulator based on Green's functions. Green's functions have been shown to befaster than the traditional finite difference and finite element-basedapproaches but have rarely been employed in thermal modeling. Hence we proposea new Green's function-based method to capture the effects of leakage power aswell as process variation analytically. We provide a closed-form solution forthe Green's function considering the effects of variation on the process,temperature, and thermal conductivity. In addition, we propose a novel way ofdealing with the anisotropicity introduced by process variation by splittingthe Green's functions into shift-variant and shift-invariant components. Sinceour solutions are analytical expressions, we were able to obtain speedups thatwere several orders of magnitude over and above state-of-the-art proposals witha mean absolute error limited to 4% for a wide range of test cases.Furthermore, our method accurately captures the steady-state as well as thetransient variation in temperature.

VarSim: A Fast Process Variation-aware Thermal Modeling Methodology Using Green's Functions