标题： 经典和全浮动FETI方法用于动脉组织的仿真 显示英文标题

标题： Classical and all-floating FETI methods for the simulation of arterial tissues

摘要： 高分辨率和解剖学上逼真的生物软组织计算机模型在理解心血管组件在健康和疾病中的功能方面起着重要作用。 然而，处理细网格以解析几何形状以及复杂的组织模型的计算工作量非常具有挑战性。 一种获得强可扩展并行求解算法的可能性是考虑有限元撕裂和连接（FETI）方法。 在本研究中，我们提出并研究了将FETI方法应用于模拟生物软组织弹性行为的可行性。 作为其中一个具体例子，我们选择动脉，它——像大多数其他生物组织一样——具有各向异性和非线性的材料特性。 我们比较了FETI方法的两种具体方法，经典方法和全浮动方法，并研究了不同预处理技术的数值行为。 与经典FETI相比，全浮动方法不仅在实现方面有优势，在许多情况下也对全局迭代求解方法的收敛性有优势。 这种行为通过数值例子进行了说明。 我们展示了线弹性模拟的结果，以显示收敛速率，正如理论所预期的那样，并展示了更复杂的非线性情况下的结果，在这种情况下，我们将一个著名的各向异性模型应用于动脉的真实几何结构。 尽管FETI方法在动脉模拟中具有广泛的应用性，但我们也将讨论一些关于材料参数依赖性的限制。 显示英文摘要

摘要： High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.