We consider the numerical simulation of the left ventricle of the human heart by a hyperelastic fiber reinforced transversely isotropic model. This is an important model problem for the understanding of the mechanical properties of the human heart but its calculation is very time consuming because the lack of fast, scalable method that is also robust with respect to the model parameters. In this paper, we propose and study a fully implicit overlapping domain decomposition method on unstructured meshes for the discretized system. The algorithm is constructed within the framework of Newton–Krylov methods with an analytically constructed Jacobian. We show numerically that the algorithm is highly parallel and robust with respect to the material parameters, the large deformation, the fiber reinforcement, and the geometry of the patient-specific left ventricle. Numerical experiments show that the algorithm scales well on a supercomputer with more than 8000 processor cores.

中文翻译：

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一种在非结构化网格上模拟左心室的高度并行隐式域分解方法

我们考虑通过超弹性纤维增强横向各向同性模型对人心脏左心室的数值模拟。这是理解人类心脏机械特性的一个重要模型问题，但它的计算非常耗时，因为缺乏快速、可扩展的方法，并且在模型参数方面也很稳健。在本文中，我们提出并研究了一种针对离散系统的非结构化网格的全隐式重叠域分解方法。该算法是在 Newton-Krylov 方法的框架内构建的，具有解析构建的雅可比行列式。我们从数值上表明，该算法在材料参数、大变形、纤维增强、以及患者特定左心室的几何形状。数值实验表明，该算法在具有 8000 多个处理器内核的超级计算机上具有良好的扩展性。