Proper Generalized Decomposition to Solve a 2D Coupled Heat-Diffusion Problem

To predict the effect of the environment on the durability of composites or polymers [3], we often have to consider coupled physical phenomena (thermo-diffuso-chemico-mechanic). Therefore, strongly coupled problems with a large number of characteristic times have to be considered. From a numerical point of view, solving these problems with the finite elements method requires the use of an incremental time scheme in which stability conditions lead to a large number of degrees of freedom and a large computation time.