Fast and accurate two-field reduced basis approximation for parametrized thermoelasticity problems

This paper concerns a two-field reduced basis algorithm for the metamodelling of parametrized one-way coupled thermoelasticity problems based on the constitutive relation error (CRE) estimation. The coupled system consists of parametrized thermal diffusion and elastostatic equations which are explicitly coupled in a one-way manner. The former can be solved in advance independently and the latter can be solved afterwards using the solution of the former. For the fast and accurate analysis of the coupled system, we developed an algorithm that can choose adaptively the number of reduced basis functions of the temperature field to approximate the CRE equality of the mechanical field. We compute approximately the upper bound for the true errors of displacement and stress fields in energy norms. To enable this, a two-field greedy sampling strategy is adopted to construct the displacement and stress fields in an efficient manner. The computational efficiency of the proposed approach is demonstrated with computing the effective coefficient of thermal expansion of heterogeneous materials.