J. V. Aguado, F. Chinesta, A. Leygue, E. C. Prendes, and A. Huerta, Deim-based PGD for parametric nonlinear model order reduction, International Conference on Adaptive Modeling and Simulation Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), pp.29-34, 2013.

Y. A. Oumeziane, M. Bart, S. Moissette, and C. Lanos, Hysteretic Behaviour and Moisture Buffering of Hemp Concrete, Transport in Porous Media, pp.515-533, 2014.
DOI : 10.2136/sssaj1980.03615995004400050002x

URL : https://hal.archives-ouvertes.fr/hal-01003199

A. H. Mohy and N. J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.3, pp.970-989, 1934.
DOI : 10.1137/09074721X

A. H. Mohy and N. J. Higham, Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, SIAM Journal on Scientific Computing, vol.33, issue.2, pp.488-511, 2011.
DOI : 10.1137/100788860

S. A. Sanea and M. F. Zedan, Improving thermal performance of building walls by optimizing insulation layer distribution and thickness for same thermal mass, Applied Energy, vol.88, issue.9, pp.3113-3124, 2011.
DOI : 10.1016/j.apenergy.2011.02.036

S. A. Sanea, M. F. Zedan, and S. A. , Effect of electricity tariff on the optimum insulation-thickness in building walls as determined by a dynamic heat-transfer model, Applied Energy, vol.82, issue.4, pp.313-330, 2005.
DOI : 10.1016/j.apenergy.2004.10.014

A. Ammar and F. Chinesta, Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decomposition, Meshfree Methods for Partial Differential Equations IV, pp.1-17
DOI : 10.1007/978-3-540-79994-8_1

URL : https://hal.archives-ouvertes.fr/hal-00289677

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2-3, pp.98-121, 2007.
DOI : 10.1016/j.jnnfm.2007.03.009

URL : https://hal.archives-ouvertes.fr/hal-01633241

A. Ammar, M. Normandin, F. Daim, D. Gonzalez, E. Cueto et al., Non incremental strategies based on separated representations: applications in computational rheology, Communications in Mathematical Sciences, vol.8, issue.3, pp.671-695, 2010.
DOI : 10.4310/CMS.2010.v8.n3.a4

URL : https://hal.archives-ouvertes.fr/hal-01007108

N. Aste, A. Angelotti, and M. Buzzetti, The influence of the external walls thermal inertia on the energy performance of well insulated buildings, Energy and Buildings, vol.41, issue.11, pp.1181-1187, 1920.
DOI : 10.1016/j.enbuild.2009.06.005

I. Axaopoulos, P. Axaopoulos, and J. Gelegenis, Optimum insulation thickness for external walls on different orientations considering the speed and direction of the wind, Applied Energy, vol.117, pp.167-175, 2014.
DOI : 10.1016/j.apenergy.2013.12.008

T. Bednar and C. Hagentoft, Analytical solution for moisture buffering effect Validation exercises for simulation tools, 7th Nordic Symposium on Building Physics, p.15, 2005.

J. Berger, M. Chhay, S. Guernouti, and M. Woloszyn, Proper generalized decomposition for solving coupled heat and moisture transfer, Journal of Building Performance Simulation, vol.96, issue.3, pp.295-311, 2015.
DOI : 10.1007/s12273-008-8106-z

URL : https://hal.archives-ouvertes.fr/hal-01819339

J. Berger and N. Mendes, An innovative method for the design of high energy performance building envelopes, Applied Energy, vol.190, pp.266-277, 1921.
DOI : 10.1016/j.apenergy.2016.12.119

J. Berger, N. Mendes, S. Guernouti, M. Woloszyn, and F. Chinesta, Review of Reduced Order Models for Heat and Moisture Transfer in Building Physics with Emphasis in PGD Approaches, Archives of Computational Methods in Engineering, vol.16, issue.9, pp.1-13, 2016.
DOI : 10.1080/17415977.2016.1160395

URL : https://hal.archives-ouvertes.fr/hal-01819330

B. Bognet, F. Bordeu, F. Chinesta, A. Leygue, and A. Poitou, Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.201-2041, 2012.
DOI : 10.1016/j.cma.2011.08.025

URL : https://hal.archives-ouvertes.fr/hal-01462825

D. E. Bond, W. W. Clark, and M. Kimber, Configuring wall layers for improved insulation performance, Applied Energy, vol.112, pp.235-245, 2013.
DOI : 10.1016/j.apenergy.2013.06.024

J. P. Boyd, Chebyshev and Fourier Spectral Methods, p.10, 2000.
DOI : 10.1007/978-3-642-83876-7

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods Fundamentals in Single Domains. Scientific Computation, p.11, 2006.

S. Chaturantabut and D. C. Sorensen, Nonlinear Model Reduction via Discrete Empirical Interpolation, SIAM Journal on Scientific Computing, vol.32, issue.5, pp.2737-2764, 1926.
DOI : 10.1137/090766498

URL : https://scholarship.rice.edu/bitstream/1911/70218/1/ChaturantabutS.pdf

S. Chen, B. Li, and Y. Sun, Chebyshev collocation spectral method for solving radiative transfer with the modified discrete ordinates formulations, International Journal of Heat and Mass Transfer, vol.88, pp.388-397
DOI : 10.1016/j.ijheatmasstransfer.2015.04.083

Y. Chen, B. Li, and J. Zhang, Spectral collocation method for natural convection in a square porous cavity with local thermal equilibrium and non-equilibrium models, International Journal of Heat and Mass Transfer, vol.96, pp.84-96, 2009.
DOI : 10.1016/j.ijheatmasstransfer.2016.01.007

F. Chinesta, A. Ammar, A. Leygue, and R. Keunings, An overview of the proper generalized decomposition with applications in computational rheology, Journal of Non-Newtonian Fluid Mechanics, vol.166, issue.11, pp.578-592, 1921.
DOI : 10.1016/j.jnnfm.2010.12.012

URL : https://hal.archives-ouvertes.fr/hal-01061441

F. Chinesta, R. Keunings, and A. Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer, p.12, 2013.
DOI : 10.1007/978-3-319-02865-1

URL : https://link.springer.com/content/pdf/bfm%3A978-3-319-02865-1%2F1.pdf

F. Chinesta, P. Ladevèze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol.69, issue.9, pp.395-404, 2011.
DOI : 10.1016/j.compscitech.2008.09.041

URL : https://hal.archives-ouvertes.fr/hal-01004940

F. Chinesta, A. Leygue, F. Bordeu, J. V. Aguado, E. Cueto et al., PGD-Based Computational Vademecum for Efficient Design, Optimization and Control, Archives of Computational Methods in Engineering, vol.51, issue.1, pp.31-59
DOI : 10.1016/j.ijheatmasstransfer.2008.02.029

URL : https://hal.archives-ouvertes.fr/hal-01515083

S. M. Cox and P. C. Matthews, Exponential Time Differencing for Stiff Systems, Journal of Computational Physics, vol.176, issue.2, pp.430-455, 2002.
DOI : 10.1006/jcph.2002.6995

A. Dalgliesh, S. Cornick, W. Maref, and P. Mukhopadhyaya, Hygrothermal Performance of Building Envelopes: Uses for 2D and 1D simulation, 10th Conference on Building Science and Technology, 2005.

G. H. Santos and N. Mendes, Simultaneous heat and moisture transfer in soils combined with building simulation, Energy and Buildings, vol.38, issue.4, pp.303-314, 2006.
DOI : 10.1016/j.enbuild.2005.06.011

T. A. Driscoll, N. Hale, and L. N. Trefethen, Chebfun Guide, p.15, 2014.

A. Dumon, C. Allery, and A. Ammar, Proper general decomposition (PGD) for the resolution of Navier???Stokes equations, Journal of Computational Physics, vol.230, issue.4, pp.1387-1407, 2011.
DOI : 10.1016/j.jcp.2010.11.010

URL : https://hal.archives-ouvertes.fr/hal-01061383

S. Gasparin, J. Berger, D. Dutykh, and N. Mendes, Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model, Journal of Building Performance Simulation, vol.109, issue.1, pp.17-26, 2018.
DOI : 10.1007/s12273-008-8106-z

URL : https://hal.archives-ouvertes.fr/hal-01513304

S. Gasparin, J. Berger, D. Dutykh, and N. Mendes, Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials, Journal of Building Performance Simulation, vol.109, issue.1, pp.129-144, 2018.
DOI : 10.1007/s12273-008-8106-z

URL : https://hal.archives-ouvertes.fr/hal-01404578

W. Gautschi, Orthogonal Polynomials: Computation and Approximation, 2004.

G. Golub and C. Van-loan, Matrix Computations. J, p.26, 1996.

W. Guo, G. Labrosse, and R. Narayanan, The Application of the Chebyshev-Spectral Method in Transport Phenomena, Lecture Notes in Applied and Computational Mechanics, vol.68, issue.9, 2012.
DOI : 10.1007/978-3-642-34088-8

M. Ibrahim, P. H. Biwole, P. Achard, E. Wurtz, and G. Ansart, Building envelope with a new aerogel-based insulating rendering: Experimental and numerical study, cost analysis, and thickness optimization, Applied Energy, vol.159, pp.490-501, 2015.
DOI : 10.1016/j.apenergy.2015.08.090

URL : https://hal.archives-ouvertes.fr/hal-01205410

H. Janssen, Simulation efficiency and accuracy of different moisture transfer potentials, Journal of Building Performance Simulation, vol.9, issue.11, pp.379-389
DOI : 10.1007/s12273-008-8106-z

H. Janssen, B. Blocken, and J. Carmeliet, Conservative modelling of the moisture and heat transfer in building components under atmospheric excitation, International Journal of Heat and Mass Transfer, vol.50, issue.5-6, pp.5-61128, 2007.
DOI : 10.1016/j.ijheatmasstransfer.2006.06.048

C. S. Kenney and A. J. Laub, A Schur--Fr??chet Algorithm for Computing the Logarithm and Exponential of a Matrix, SIAM Journal on Matrix Analysis and Applications, vol.19, issue.3, pp.640-663, 1998.
DOI : 10.1137/S0895479896300334

M. Labat, C. Magniont, N. Oudhof, and J. Aubert, From the experimental characterization of the hygrothermal properties of straw-clay mixtures to the numerical assessment of their buffering potential, Building and Environment, vol.97, pp.69-81, 1920.
DOI : 10.1016/j.buildenv.2015.12.004

URL : https://hal.archives-ouvertes.fr/hal-01785406

P. Ladevèze, Sur une famille d'algorithmes en mécanique des structures. Comptes-rendus des séances de l'Académie des sciences. Série 2, Mécanique-physique, chimie, sciences de l'univers, sciences de la terre, pp.41-44, 1985.

H. Lamari, A. Ammar, A. Leygue, and F. Chinesta, On the solution of the multidimensional Langer's equation using the proper generalized decomposition method for modeling phase transitions, Modelling and Simulation in Materials Science and Engineering, vol.20, issue.1, pp.7-15, 2012.
DOI : 10.1088/0965-0393/20/1/015007

B. Li, Y. Sun, and Y. Yu, Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer, International Journal of Heat and Mass Transfer, vol.51, issue.25-26, pp.25-265887, 2008.
DOI : 10.1016/j.ijheatmasstransfer.2008.04.048

A. V. Luikov, Heat and mass transfer in capillary-porous bodies, 1966.
DOI : 10.1016/s0065-2717(08)70098-4

J. Ma, B. Li, and J. R. Howell, Thermal radiation heat transfer in one- and two-dimensional enclosures using the spectral collocation method with full spectrum k-distribution model, International Journal of Heat and Mass Transfer, vol.71, pp.35-43, 2009.
DOI : 10.1016/j.ijheatmasstransfer.2013.12.009

N. Mendes, M. Chhay, J. Berger, and D. Dutykh, Numerical methods for diffusion phenomena in building physics, pp.2017-2027
DOI : 10.7213/978868324455

N. Mendes and P. C. Philippi, A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients, International Journal of Heat and Mass Transfer, vol.48, issue.1, pp.37-51, 2005.
DOI : 10.1016/j.ijheatmasstransfer.2004.08.011

C. Moler and C. Van-loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, SIAM Review, vol.45, issue.1, pp.3-49, 1934.
DOI : 10.1137/S00361445024180

S. Motsa, On the New Bivariate Local Linearisation Method for Solving Coupled Partial Differential Equations in Some Applications of Unsteady Fluid Flows with Heat and Mass Transfer, Mass Transfer -Advancement in Process Modelling. InTech, 2009.
DOI : 10.5772/60444

D. Néron and P. Ladevèze, Proper Generalized Decomposition for Multiscale and??Multiphysics Problems, Archives of Computational Methods in Engineering, vol.193, issue.1???4, pp.351-372, 2010.
DOI : 10.1016/j.cma.2003.11.006

S. Niroomandi, I. Alfaro, E. Cueto, and F. Chinesta, Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models, Computer Methods and Programs in Biomedicine, vol.105, issue.1, pp.1-12, 2012.
DOI : 10.1016/j.cmpb.2010.06.012

URL : https://hal.archives-ouvertes.fr/hal-01004972

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.45-484521, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

M. Ozel, Effect of wall orientation on the optimum insulation thickness by using a dynamic method, Applied Energy, vol.88, issue.7, pp.2429-2435, 2011.
DOI : 10.1016/j.apenergy.2011.01.049

M. N. Ozisik, Heat conduction, p.17, 1993.

A. Pasban, H. Sadrnia, M. Mohebbi, and S. A. Shahidi, Spectral method for simulating 3D heat and mass transfer during drying of apple slices, Journal of Food Engineering, vol.212, pp.201-212, 2009.
DOI : 10.1016/j.jfoodeng.2017.05.013

R. Peyret, Spectral methods for incompressible viscous flow, p.11, 2002.
DOI : 10.1007/978-1-4757-6557-1

J. R. Philip, D. A. De, and . Vries, Moisture movement in porous materials under temperature gradients, Transactions, American Geophysical Union, vol.73, issue.2, pp.222-232, 1957.
DOI : 10.1097/00010694-195202000-00002

E. Pruliere, F. Chinesta, and A. Ammar, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Mathematics and Computers in Simulation, vol.81, issue.4, pp.791-810, 2010.
DOI : 10.1016/j.matcom.2010.07.015

URL : https://hal.archives-ouvertes.fr/hal-00704427

H. Rafidiarison, R. Rémond, and E. Mougel, Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials, Building and Environment, vol.89, pp.356-368, 2015.
DOI : 10.1016/j.buildenv.2015.03.008

URL : https://hal.archives-ouvertes.fr/hal-01598447

C. Ramreddy, P. A. Narayana, and S. S. Motsa, A spectral relaxation method for linear and non-linear stratification effects on mixed convection in a porous medium, Applied Mathematics and Computation, vol.268, pp.991-1000, 2009.
DOI : 10.1016/j.amc.2015.07.007

C. Rode and R. H. Peuhkur, The Concept of Moisture Buffer Value of Building Materials and its Application in Building Design, Healthy Buildings, pp.57-62, 2006.

S. Roels, J. Carmeliet, and H. Hens, Modelling Unsaturated Moisture Transport in Heterogeneous Limestone, Transport in Porous Media, pp.333-350, 2003.

L. F. Shampine and M. W. Reichelt, The MATLAB ODE Suite. SIAM J. Sci. Comput, vol.18, issue.17, pp.1-22, 1997.

L. N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, 1996.

M. M. Waldrop, The chips are down for Moore???s law, Nature, vol.530, issue.7589, pp.144-147, 2006.
DOI : 10.1038/530144a

C. Wang, Z. Qiu, and Y. Yang, Collocation methods for uncertain heat convection-diffusion problem with interval input parameters, International Journal of Thermal Sciences, vol.107, pp.230-236
DOI : 10.1016/j.ijthermalsci.2016.04.012

M. Woloszyn and C. Rode, Tools for performance simulation of heat, air and moisture conditions of whole buildings, Building Simulation, vol.2, issue.112, pp.5-24, 2008.
DOI : 10.1002/bapi.200710028

URL : https://hal.archives-ouvertes.fr/hal-00353433

J. Yuan, C. Farnham, K. Emura, and M. A. Alam, Proposal for optimum combination of reflectivity and insulation thickness of building exterior walls for annual thermal load in Japan, Building and Environment, vol.103, pp.228-237, 2016.
DOI : 10.1016/j.buildenv.2016.04.019

. Gasparin, Campus Scientifique , F-73376 Le Bourget-du-Lac Cedex, France and Thermal Systems Laboratory, Mechanical Engineering Graduate Program, pp.80215-901

J. Berger, Campus Scientifique , F-73376 Le Bourget-du-Lac Cedex, France E-mail address: Berger.Julien@univ-smb.fr URL: https://www.researchgate.net/profile, p.73000

F. Chambéry and L. , Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex, France E-mail address: Denys.Dutykh@univ-smb.fr URL: http://www.denys-dutykh, pp.80215-901