经典和全浮动FETI方法在动脉组织模拟中的应用
Classical and all-floating FETI methods for the simulation of arterial tissues
AI总结：
本文提出并研究了FETI方法在生物软组织弹性行为模拟中的应用，比较了经典和全浮动FETI方法的数值性能，并展示了线性和非线性模拟结果。
摘要：
高分辨率和解剖真实性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中起重要作用。然而，处理细网格以解析几何和复杂组织模型的计算工作量非常具有挑战性。一种可能的解决方案是考虑有限元撕裂和连接（FETI）方法。本文提出并研究了FETI方法用于模拟生物软组织弹性行为的应用。作为具体例子，我们选择动脉，其特点是各向异性和非线性材料特性。我们比较了FETI方法的两种特定方法，经典和全浮动，并研究了不同预条件技术的数值行为。与经典FETI相比，全浮动方法不仅在实现上有优势，而且在许多情况下也对全局迭代求解方法的收敛性有帮助。这种行为通过数值示例进行说明。我们展示了线性弹性模拟的结果，以显示理论预期的收敛率，并展示了更复杂的非线性情况下的结果，其中我们应用了已知的各向异性模型到动脉的真实几何结构上。尽管FETI方法在动脉模拟中有广泛的应用，我们还将讨论其在材料参数依赖性方面的某些限制。
英文摘要：
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.
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