Dual-primal FETI (FETI-DP) preconditioners 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 and without 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:二维生物模型(FETI-DP)的双重原始FETI(FETI-DP)先决条件为 2D 生物模型(PETI-DP) 。 模型的配方是混合的无限元素,作为支撑点问题。 置换 $\ mathbf{u} 和 Darcy 通量流 $\ mathbf{z} 代表着 $ P$ 1 profile 连续元素和 pore-press $ p$, 单向固定元素 $0 profile 常量元素 。 我们已经测试了 FETI-DP 的功能, 使用和不使用 dirichlet 预设元素 。 数字实验显示, 产生的平行算法在可压缩弹性性中具有可渗透性, 以及几乎不可压缩弹性的 。