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

• Published in: Computational mechanics Vol. 66; no. 6; pp. 1461 - 1475
• Main Authors: Jiang, Yi, Chen, Rongliang, Cai, Xiao-Chuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Cardiology; Classical and Continuum Physics; Computational Science and Engineering; Computer simulation; Domain decomposition methods; Engineering; Fiber reinforced materials; Fiber reinforcement; Heart; Mathematical models; Mechanical properties; Methods; Microprocessors; Numerical analysis; Original Paper; Parameters; Robustness (mathematics); Theoretical and Applied Mechanics; Parallel computing; Fiber-reinforced hyperelasticity; Domain decomposition; Left ventricle; Finite element
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-020-01912-3

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.