Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems

Abstract: This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of reduced basis space. On the other hand, for the evaluation of the modal coefficients, we use two different methodologies: the one based on the Galerkin projection (G) and the other one based on Artificial Neural Network (ANN). We aim at comparing POD-G and POD-ANN in terms of relevant features including errors and computational efficiency. In this context, both physical and geometrical parametrization are considered. We also carry out a validation of the Full Order Model (FOM) based on customized benchmarks in order to provide a complete computational pipeline. The framework proposed is applied to a relevant industrial problem related to the investigation of thermomechanical phenomena arising in blast furnace hearth walls. Keywords: Thermomechanical problems, Finite element method, Proper orthogonal decomposition, Galerkin projection, Artificial neural network, Geometric and physical parametrization, Blast furnace.