SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page B381-B404, January 2021.
A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field domain decomposition framework in which independent variables are introduced at the interfaces generated in the process of decoupling the original problem on the whole network into a set of fracture-local problems. A PDE-constrained formulation is then used to enforce compatibility conditions at the interfaces. The combination of the three-field domain decomposition and of the optimization-based coupling strategy results in a novel method which can handle nonconforming meshes, independently built on each geometrical object of the computational domain, and ensures a local mass conservation property at fracture intersections, which is of paramount importance for hydrogeological applications. An iterative solver is devised for the method, suitable for parallel implementation on parallel computing architectures.

中文翻译：

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非一致性网格上裂缝网络流动模拟的三场优化公式

SIAM科学计算杂志，第43卷，第2期，第B381-B404页，2021年1月。
提出了一种新的数值方案，用于复杂离散裂缝网络中的流动计算。该方法基于三场域分解框架，其中在将整个网络上的原始问题解耦为一组局部裂缝问题的过程中，在生成的接口处引入自变量。然后使用受PDE约束的公式在接口处强制执行兼容性条件。三场域分解和基于优化的耦合策略的结合产生了一种新方法，该方法可以独立处理基于计算域的每个几何对象的不合格网格，并确保裂缝相交处的局部质量守恒特性，这对于水文地质应用至关重要。