New model reduction technique for a class of parabolic partial differential equations (temperature distribution)

A model reduction (or lumping) technique for a class of parabolic-type partial differential equations is given, and its application is discussed. The frequency response of the temperature distribution in any multilayer solid is developed and given by a matrix expression. The distributed transfer functions (DTFs) between the surface variables and the ambient variables are given. The proposed method is based on the special high-frequency properties of these DTFs. The rational fraction expansion is compared with the lumping technique. Numerical examples from real-time applications are given.<>