POD–DEIM model order reduction for nonlinear heat and moisture transfer in building materials

Abstract

In this paper, the proper orthogonal decomposition (POD) method and the discrete empirical interpolation method (DEIM) are combined to construct a reduced-order model for a cost-optimal simulation of heat and moisture transfer in building materials. The POD-DEIM performance is assessed via two applications: a relatively simple case study on nonlinear heat conduction and a more complex case study on nonlinear moisture redistribution. In both, the results of the POD-DEIM model are compared to results from POD and finite volume methods simulations, to evaluate the accuracy of the POD-DEIM as a function of the numbers of construction modes and interpolation points. Also, as the number of POD construction modes and DEIM interpolation points does not entirely represent the computational cost of different models, the accuracies of the different models are compared as a function of the respective calculation times, to provide a fair comparison of their computational performances. Further, the use of POD-DEIM to simulate a problem different from the POD training snapshot simulation is investigated. The outcomes show that when a rather highly accurate result is desired, POD-DEIM model is capable of reducing the computational cost relative to POD and FVM.

KEYWORDS:

• Proper orthogonal decomposition
• discrete empirical interpolation method
• finite volume method
• heat and moisture transfer
• model order reduction
• building hygrothermal performance

Acknowledgement

This work was supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No 637268 (RIBuild).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the European Union’s Horizon 2020 research and innovation program under grant agreement [No 637268] (RIBuild); H2020 European Institute of Innovation and Technology.