关于非均质多孔介质中流动的自适应BDDC方法
On adaptive BDDC for the flow in heterogeneous porous media
AI总结：
本文提出一种基于BDDC的自适应方法用于求解非均质多孔介质单相流动，通过三步求解通量与压力，并引入自适应算法选择通量约束，在SPE 10基准测试中显著减少了共轭梯度法迭代次数。
摘要：
我们研究了一种基于平衡区域分解约束（BDDC）的方法，用于求解非均质多孔介质中单相流动的数值解。该方法同时求解通量和压力变量。通量求解分三步进行：首先进行粗求解，随后进行子区域求解，最后使用带BDDC预处理器的共轭梯度法寻找无散度通量校正和压力。我们的主要贡献是应用了自适应算法来选择通量约束。该方法在来自第10届SPE比较解项目（SPE 10）的基准问题上展示了其性能。2D和3D数值实验表明，该方法的前两步表现出一些数值粗化性质，最后一步的自适应预处理器允许在极小的额外成本下显著减少共轭梯度法的迭代次数。
英文摘要：
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection of flux constraints. Performance of the method is illustrated on the benchmark problem from the 10th SPE Comparative Solution Project (SPE 10). Numerical experiments in both 2D and 3D demonstrate that the first two steps of the method exhibit some numerical upscaling properties, and the adaptive preconditioner in the last step allows a significant decrease in number of iterations of conjugate gradients at a small additional cost.
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