# Solving nonlinear diffusive problems in buildings by means of a Spectral Reduced-Order Model

## TL;DR

This paper introduces a Spectral Reduced-Order Model for simulating nonlinear moisture transfer in building materials, achieving high accuracy and significant computational efficiency compared to traditional methods.

## Contribution

The paper presents a novel Spectral ROM approach for nonlinear diffusive problems in buildings, demonstrating superior accuracy and computational speed over classical schemes.

## Key findings

- Spectral ROM accurately simulates moisture transfer in porous materials.
- The method reduces CPU time by up to 100 times in nonlinear cases.
- Performance is validated against classical Euler and Crank-Nicolson schemes.

## Abstract

This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large original models. Their performance - in terms of accuracy, complexity reduction and CPU time reduction - are discussed for linear and nonlinear cases of moisture diffusive transfer through single and multi-layered one-dimensional domains, considering highly moisture-dependent properties. Results show that the Spectral reduced-order model approach enables to simulate accurately the field of interest. Furthermore, numerical gains become particularly interesting for nonlinear cases since the proposed method can drastically reduce the computer run time, by a factor of 100, when compared to the traditional Crank-Nicolson scheme for one-dimensional applications.