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Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation

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Abstract

A goal-oriented a-posteriori error estimator is developed for transient coupled thermo-hydro-mechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goal-oriented error estimate is derived based on explicitly-computed weak residual of the primal problem and implicitly-computed adjoint solution associated with the QoI. The time-dependence of the coupled THM system poses an additional complexity as the auxiliary adjoint problem evolves backwards in time. The error estimator guides a greedy adaptive procedure that constructs progressively an optimal reduced basis by smartly selecting snapshot points over a given parametric training sample. The reduced basis obtained is used to drastically reduce the coupled system spatial degrees of freedom by several orders of magnitude. The computational gain obtained from the developed methodology is demonstrated through applications in 2D and 3D parametrized problems simulating the evolution of coupled THM processes in rock masses.

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Acknowledgements

We acknowledge the Funding support from the European Commission Education, Audiovisual and Culture Executive Agency (EACEA) under Erasmus Mundus Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED), FPA 2013-0043. S. Zlotnik would like to thank the Funding from the Generalitat de Catalunya 2017-SGR-1278, the Project DPI2017-85139-C2-2-R funded by the Spanish Ministry and the Project H2020-RISE MATHROCKS GA No. 777778. T.J. Massart acknowledges the support of FRS-FNRS through Grant 26033553 EnLightenIt. We would also like to thank SCK-CEN for the valuable interactions related to coupled systems in nuclear waste repository applications.

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Authors and Affiliations

  1. Building, Architecture and Town Planning, Structural and Material Computational Mechanics Group (BATIR-SMC), Université libre de Bruxelles, CP 194/2, Avenue F.D. Roosevelt 50, 1050, Brussels, Belgium

    Ygee Larion & Thierry J. Massart

  2. Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, Campus Nord UPC, 08034, Barcelona, Spain

    Ygee Larion, Sergio Zlotnik & Pedro Díez

  3. International Centre for Numerical Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio Zlotnik & Pedro Díez

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  1. Ygee Larion
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  2. Sergio Zlotnik
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Correspondence to Thierry J. Massart.

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Larion, Y., Zlotnik, S., Massart, T.J. et al. Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation. Comput Mech 66, 559–573 (2020). https://doi.org/10.1007/s00466-020-01865-7

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