A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes
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ORIGINAL PAPER
A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes Yi Jiang1,2 · Rongliang Chen1,2 · Xiao-Chuan Cai3 Received: 2 May 2020 / Accepted: 17 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Fiber-reinforced hyperelasticity · Left ventricle · Domain decomposition · Finite element · Parallel computing
1 Introduction Computational modeling is used increasingly to study the mechanical properties of the human heart [10,14,28,39,41]. To have more realistic simulations, sophisticated material models are being considered and very fine meshes are used to discretize the highly nonlinear partial differential equations. Such simulations are extremely time consuming and require highly parallel algorithms that are also robust with respect the material properties. In this paper, we develop a domain decomposition method for the simulation of the left ventricle described by a hyperelastic model reinforced by transversely isotropic fibers.
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Rongliang Chen [email protected] Xiao-Chuan Cai [email protected]
1
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong, China
2
Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing, Shenzhen, Guangdong, China
3
Department of Mathematics, University of Macau, Macau, China
Several parallel algorithms for cardiac mechanics have been introduced in the past few years. Among them, one category is developed based on structured or mapped structured grids that are relatively easy to parallelize. For example, in [34], an electro-mechanical model problem was investigated by Reumann et al. on a structured grid, the calculation uses 16,000 processor cores for a mesh with 128 million cells. Pavarino et al. developed a Newton-Krylov type method for a cardiac mechanical model discretized by finite element methods on mapped regular grids, the resulting problem is solved by either an algebraic multigrid [12] or BDDC method [13,31,32]. The method scales well f
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