A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning

JOURNAL OF COMPUTATIONAL PHYSICS

卷:383

Article

Liu, Ju^1,2  Marsden, Alison L.^1,2 

[1] Stanford Univ, Dept Pediat Cardiol, Bioengn, Clark Ctr E1-3 318 Campus Dr, Stanford, CA 94305 USA

[2] Stanford Univ, Inst Computat & Math Engn, Clark Ctr E1-3 318 Campus Dr, Stanford, CA 94305 USA

关键词: Variational multiscale method;    Saddle-point problem;    Nested iterative method;    Block preconditioner;    Anisotropic incompressible hyperelasticity;    Arterial wall model;   

DOI  :  10.1016/j.jcp.2019.01.019

来源: Elsevier

【 摘 要 】

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed in [1]. The numerical scheme is constructed based on the variational multiscale formulation and the generalized-alpha method. Within the nonlinear solution procedure, a block factorization is performed for the consistent tangent matrix to decouple the kinematics from the balance laws. Within the linear solution procedure, another block factorization is performed to decouple the mass balance equation from the linear momentum balance equations. A nested block preconditioning technique is proposed to combine the Schur complement reduction approach with the fully coupled approach. This preconditioning technique, together with the Krylov subspace method, constitutes a novel iterative method for solving hyper-elastodynamics. We demonstrate the efficacy of the proposed preconditioning technique by comparing with the SIMPLE preconditioner and the one-level domain decomposition preconditioner. Two representative examples are studied: the compression of an isotropic hyperelastic cube and the tensile test of a fully-incompressible anisotropic hyperelastic arterial wall model. The robustness with respect to material properties and the parallel performance of the preconditioner are examined. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free