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In this work, we discuss the parametric modeling for the (electro)-thermal analysis of components of nanoelectronic structures and automatic model order reduction of the consequent parametric models. Given the system matrices at different values of the parameters, we introduce a simple method of extracting system matrices which are independent of the parameters, so that parametric models of a class of linear parametric problems can be constructed. Then the reduced-order models of the large-scale parametric models are automatically obtained using a posteriori output error bounds for the reduced-order models. Simulations of both thermal and electro-thermal systems confirm the validity of the proposed methods.

Parametric modeling and model order reduction for (electro-)thermal analysis of nanoelectronic structures