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Accelerating the solution of linear systems appearing in two-phase reservoir simulation by the use of POD-based deflation methods
Computational Geosciences ( IF 2.1 ) Pub Date : 2021-06-07 , DOI: 10.1007/s10596-021-10041-6
Gabriela Berenice Diaz Cortés , Cornelis Vuik , Jan-Dirk Jansen

We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.



中文翻译:

使用基于 POD 的放气方法加速两相油藏模拟中出现的线性系统的求解

我们探索并开发了一种基于适当正交分解 (POD) 的放气方法,用于解决病态线性系统,出现在通过高度异质多孔介质的两相流模拟中。我们加速了预条件共轭梯度 (PCG) 方法的收敛,实现了高达五个因子的加速。所提出方法的前期额外计算成本取决于紧缩向量的数量。基于POD的紧缩方法针对特定问题和线性求解器进行了测试;然而,它可以应用于各种瞬态问题,并与多种求解器相结合,例如 Krylov 子空间和多重网格方法。

更新日期:2021-06-07
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