Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms are developed for a 2D Biot model. The model is formulated with mixed-finite elements as a saddle-point problem. The displacement $\mathbf{u}$ and the Darcy flux flow $\mathbf{z}$ are represented with $P_1$ piecewise continuous elements and pore-pressure $p$ with $P_0$ piecewise constant elements, {\it i.e.}, overall three fields with a stabilizing term. We have tested the functionality of FETI-DP with Dirichlet preconditioners. Numerical experiments show a signature of scalability of the resulting parallel algorithm in the compressible elasticity with permeable Darcy flow as well as almost incompressible elasticity.

翻译：本文针对二维Biot模型发展了双-原始有限元撕裂与互连（FETI-DP）算法。该模型采用混合有限元方法构造为鞍点问题。位移$\mathbf{u}$和达西通量$\mathbf{z}$使用$P_1$分片连续单元表示，孔隙压力$p$则采用$P_0$分片常数单元，即整体上采用含稳定项的三场格式。我们测试了带有Dirichlet预条件子的FETI-DP算法的功能。数值实验表明，对于可压缩弹性体中的可渗透达西流以及几乎不可压缩弹性体，所提出的并行算法具有可扩展性的典型特征。