论文标题
用于多个网络孔行弹性模型的杂交不连续的Galerkin方法与医疗应用
Hybridized Discontinuous Galerkin Methods for a Multiple Network Poroelasticity Model with Medical Applications
论文作者
论文摘要
准静态多个网络毛弹性理论（MPET）模型最初是在地球力学背景下引入的，最近在医学中发现了新的应用。实际上，MPET方程中的参数可能会因几个数量级而有所不同，这使其稳定的离散化和快速解决方案成为具有挑战性的任务。在这里，为MPET模型提出了一种新的有效的参数杂交杂交的不连续的Galerkin方法，该方法还具有流体质量保护。其稳定性分析对于离散问题的适当性至关重要，并且得出了具有成本效益的快速参数前预定器的稳定性分析。我们为人脑的4网络MPET模型提供了一系列数值计算，该模型支持新算法的性能。
The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several orders of magnitude which makes their stable discretization and fast solution a challenging task. Here, a new efficient parameter-robust hybridized discontinuous Galerkin method, which also features fluid mass conservation, is proposed for the MPET model. Its stability analysis which is crucial for the well-posedness of the discrete problem is performed and cost-efficient fast parameter-robust preconditioners are derived. We present a series of numerical computations for a 4-network MPET model of a human brain which support the performance of the new algorithms.
