发表机构
University of Bergen; University of Duisberg-Essen; NORCE Norwegian Research AS（卑尔根大学; 杜伊斯堡-埃森大学; NORCE挪威研究有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出线性Robin型区域分解格式求解Richards方程混合形式，通过非重叠分解隔离非均质材料，采用L格式线性化与混合有限元离散，严格证明收敛性，二维/三维算例验证了效率与鲁棒性。
AI 中文摘要
本文提出了一种线性Robin型区域分解格式，用于求解控制变饱和多孔介质中流动的Richards方程混合形式（mLRDD格式）。假设多孔介质高度非均质，由多个不同材料的块体/层组成，我们采用非重叠区域分解将各材料隔离，使每个子域内条件近似均匀。Richards方程在时间上采用向后欧拉离散，并使用L格式线性化。随后推导了与混合形式一致的Robin型界面条件以耦合各子域。空间离散采用混合有限元，确保局部质量守恒，并提供与Robin条件一致的通量变量。严格证明了所提格式的收敛性。给出了二维/三维非均质多域数值算例，验证了格式的效率和鲁棒性，并对理论收敛结果进行了数值验证。
英文摘要
In this work, we present a linear Robin-type domain decomposition scheme for solving the mixed formulation of Richards' equation (mLRDD-scheme), governing flow in variably saturated porous media. Assuming a highly heterogeneous porous medium consisting of multiple blocks/layers of distinct materials, we apply non-overlapping domain decomposition to isolate individual materials, yielding near-homogeneous conditions within each subdomain. Richards' equation is discretized in time by backward Euler and linearized using the L-scheme. A Robin-type interface condition, consistent with the mixed formulation, is then derived to couple the subdomains. For spatial discretization, mixed finite elements are employed, ensuring local mass conservation and providing the flux variables consistent with the Robin condition. The convergence of the proposed scheme is rigorously proved. Heterogeneous, multidomain numerical examples in 2D/3D are presented to demonstrate the efficiency and robustness of the scheme, along with numerical validation of the theoretical convergence results.
