Solving parametric problems in building renovation with a spectral reduced-order method

In this paper, the spectral method is developed as a reduced-order model for the solution of parametric problems within the building refurbishment framework. We propose to use the spectral reduced-order method to solve parametric problems in an innovative way, integrating the unknown parameter as one of the coordinates of the decomposition. The residual is minimized combining the Tau-Galerkin method with the Collocation approach. The developed method is evaluated in terms of accuracy and reduction of the computational time in three different cases. The dynamic behaviour of unidimensional moisture diffusion is investigated. The cases focus on solving parametric problems in which the solution depends on space, time, diffusivity and material thickness. Results highlight that the parametric spectral reduced-order method provides accurate solutions and can reduce 10 times the degree of freedom of the solution. It allows efficient computation of the physical phenomena with a lower error when compared to traditional approaches.

Automated summary

In this paper, the spectral method is developed as a reduced-order model for solving parametric problems within the building refurbishment framework. The proposed spectral reduced-order method integrates the unknown parameter as one of the coordinates of the decomposition and minimizes the residual using the Tau-Galerkin method and Collocation approach. The method is evaluated in terms of accuracy and computational time reduction in three different cases, showing accurate solutions and significant reduction in degrees of freedom.