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A Reduced Basis Method for a PDE-constrained optimization formulation in Discrete Fracture Network flow simulations

机译:用于离散裂缝网络流模拟的PDE受限优化制剂的基础方法

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In classic Reduced Basis (RB) framework, we propose a new technique for the offline greedy error analysis which relies on a residual-based a posteriori error estimator. This approach is as an alternative to classical a posteriori RB estimators, avoiding a discrete inf-sup lower bound estimate. We try to use less common ingredients of the RB framework to retrieve a better approximation of the RB error, such as the estimation of the distance between the continuous solution and the reduced one. In particular we focus on the application of the reduction model for the flow simulations in underground fractured media, in which high accurate simulations suffer for the complexity of the domain geometry. Finally, some numerical tests are assessed to confirm the viability and the efficacy of the technique proposed.
机译:在经典减少的基础(RB)框架中,我们提出了一种新的贪婪误差分析的新技术,依赖于基于残余的后验误差估计器。 这种方法是典型的后验RB估计器的替代方案,避免了离散的INF-SUP下限估计。 我们尝试使用RB框架的少量常见成分来检索RB误差的更好近似,例如估计连续解决方案和减小的距离之间的距离。 特别地,我们专注于在地下裂缝介质中的流量模拟的减少模型的应用,其中高精度模拟对于域几何的复杂性受到影响。 最后,评估了一些数值测试以确认了所提出的技术的生存能力和功效。

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