Novel approach for the extraction of nonlinear compact thermal models

A novel approach for extracting dynamic compact thermal models from nonlinear heat diffusion equations, which take into account the temperature dependence of thermal properties, is presented. In such Model Order Reduction method, the nonlinear heat diffusion equation is projected onto the space spanned by a few terms in the Volterra's series expansion of the solution. Such projection is performed by a novel structure-preserving hyper-reduction algorithm. The resulting method is very efficient, and can lead to very accurate compact thermal models, with unprecedented levels of simplicity. Moreover such models can be extracted for practically any regular temperature dependence of heat capacity, thermal conductivity and heat exchange coefficients. The method has been validated through the analysis of a complex ultra thin stacked chip module.