论文标题
关于二阶隐式时间步变方案产生的时间二散动态多个网络毛弹性系统的稳定性
On the stability of time-discrete dynamic multiple network poroelasticity systems arising from second-order implicit time-stepping schemes
论文作者
论文摘要
经典的生物分子的理论为描述流体饱和培养基中弹性波的传播的完全动态的孔隙弹性模型提供了基础。多个网络毛弹性理论（MPET）认为，弹性矩阵（实心）可以被一个或几个（$ n \ ge1 $）叠加的相互作用的单流体网络渗透，具有不同特征。因此，单个网络（经典BIOT）模型可以视为MPET模型的特殊情况。我们分析了应用于MPET模型的变异公式的二阶隐式时间步进方案产生的时间二散系统的稳定性，并证明具有独立于所有模型参数的常数的INF-SUP条件。此外，我们表明，针对强烈保守空间离散的家族获得的完全离散的模型在空间离散参数方面也均匀稳定。这些结果所保留的规范是参数射击预处理的基础。
The classical Biot's theory provides the foundation of a fully dynamic poroelasticity model describing the propagation of elastic waves in fluid-saturated media. Multiple network poroelastic theory (MPET) takes into account that the elastic matrix (solid) can be permeated by one or several ($n\ge1$) superimposed interacting single fluid networks of possibly different characteristics; hence the single network (classical Biot) model can be considered as a special case of the MPET model. We analyze the stability properties of the time-discrete systems arising from second-order implicit time stepping schemes applied to the variational formulation of the MPET model and prove an inf-sup condition with a constant that is independent of all model parameters. Moreover, we show that the fully discrete models obtained for a family of strongly conservative space discretizations are also uniformly stable with respect to the spatial discretization parameter. The norms in which these results hold are the basis for parameter-robust preconditioners.
