Reduced Order Methods

Abstract

In building physics, as mentioned in Chaps. 2 and 3, numerical models used to predict heat and moisture transfer involve different characteristic time and lengths. Simulation of building behavior is generally analyzed on a time scale of 1 year (or more). However, the phenomena and particularly the boundary conditions evolve in seconds. The geometric configurations of the buildings require three-dimensional modeling of a facade of several meters. Furthermore, when dealing with heat and moisture, the nonlinear behaviors of the materials might be taken into consideration. Thus, the numerical model may require fine discretization of space and time domains to solve large algebraic systems. Model reduction be used to approach the solution of the problem in a reduced space dimension. This chapter aims at introducing model reduction methods to be applied to diffusion problems in applications of building physics.