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.

中文翻译：

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为具有面向目标的误差估计的热-水-机械耦合系统构建经过认证的简化基础

针对瞬态耦合热-水-机械 (THM) 参数问题开发了一种面向目标的 a-posteriori 误差估计器，该问题通过简化的基近似来解决。估算器评估某些特定感兴趣数量 (QoI) 的误差。面向目标的误差估计是基于显式计算的原始问题的弱残差和隐式计算的与 QoI 相关的伴随解导出的。耦合 THM 系统的时间依赖性带来了额外的复杂性，因为辅助伴随问题随时间向后演化。误差估计器引导贪婪的自适应过程，该过程通过在给定的参数训练样本上巧妙地选择快照点来逐步构建最佳简化基础。所获得的简化基用于将耦合系统的空间自由度大幅降低几个数量级。通过在 2D 和 3D 参数化问题中的应用来模拟岩体中耦合 THM 过程的演变，证明了从开发的方法中获得的计算增益。