Effective method for construction of low-dimensional models for heat transfer process

A low-dimensional model based on the method of proper orthogonal decomposition (POD) and the method of polyargumental systems (MPS) for thermal conductivity problems with strongly localized source of heat has been presented. The key aspect of these methods is that they enable to avoid weak point of other projection methods, which consists in a priori choice of basis functions. It enables us to use the MPS method and the POD method as convenient means to construct low-dimensional models of heat and mass transfer problems.