Advanced harmonic techniques for solving the transient heat equation

Abstract

Simulation-based management of processes has always been a big challenge because of the difficulty to merge two apparently opposed idea s: the real time handling demanded by the process, and the traditionally strong time c onsumption linked to the sim- ulation. However, very often processes are monitored or con trolled by performing relatively few measures on some specific points of the domain. Then, one s trategy for accelerating the simulation might be based on trying to compute the respon se only where it is needed. For this reason this work revisits a classical technique, th e harmonic analysis, which is combined with recent model reduction techniques giving pla ce to an advanced harmonic technique for solving linear parabolic equations and, in pa rticular, the transient heat equa- tion. Thanks to fact that Reciprocity principle applies in t he frequency domain, the solu- tion can be computed where it is of interest by performing an i nexpensive postprocessing of a pre-computed transfer function. This transfer functio n, that must be valid for a suffi- ciently large range of frequencies, is efficiently computed b y using the Proper Generalized Decomposition method.