A Nonlinear Elimination Preconditioned Newton Method with Applications in Arterial Wall Simulation

  • Shihua GongEmail author
  • Xiao-Chuan CaiEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


Arterial wall can be modeled by a quasi-incompressible, anisotropic and hyperelastic equation that allows large deformation. Most existing nonlinear solvers for the steady hyperelastic problem are based on pseudo time stepping, which often requires a large number of time steps especially for the case of large deformation. It is also reported that the quasi-incompressibility and high anisotropy have negative effects on the convergence of both Newton’s iteration and the linear Jacobian solver. In this paper, we propose and study a nonlinearly preconditioned Newton method based on nonlinear elimination to calculate the steady solution directly without pseudo time integration. We show numerically that the nonlinear elimination preconditioner accelerates Newton’s convergence in cases with large deformation, quasi-incompressibility and high anisotropy.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingPeople’s Republic of China
  2. 2.Department of Computer ScienceUniversity of Colorado BoulderBoulderUSA

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