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A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes

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Abstract

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.

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Acknowledgements

This work was partially supported by the National Key R&D Program of China 2016YFB0200601, Shenzhen grants under ZDSYS201703031711426 and JCYJ20180507182506416, and the Strategic Priority Research Program of Chinese Academy of Sciences, Grant No. XDC01040100.

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Authors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong, China

    Yi Jiang & Rongliang Chen

  2. Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing, Shenzhen, Guangdong, China

    Yi Jiang & Rongliang Chen

  3. Department of Mathematics, University of Macau, Macau, China

    Xiao-Chuan Cai

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  1. Yi Jiang
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  2. Rongliang Chen
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  3. Xiao-Chuan Cai
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Correspondence to Rongliang Chen.

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Jiang, Y., Chen, R. & Cai, XC. A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes. Comput Mech 66, 1461–1475 (2020). https://doi.org/10.1007/s00466-020-01912-3

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