Liu Ju, Marsden Alison L
Department of Pediatrics (Cardiology), Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA.
J Comput Phys. 2019 Apr 15;383:72-93. doi: 10.1016/j.jcp.2019.01.019. Epub 2019 Feb 1.
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- 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.
基于[1]中最近开发的一种新型连续体公式，我们为超弹性动力学开发了一种稳健且高效的迭代方法。该数值格式基于变分多尺度公式和广义方法构建。在非线性求解过程中，对一致切线矩阵进行块分解，以使运动学与平衡定律解耦。在线性求解过程中，进行另一次块分解，以使质量平衡方程与线性动量平衡方程解耦。提出了一种嵌套块预处理技术，将舒尔补约简方法与完全耦合方法相结合。这种预处理技术与克里洛夫子空间方法一起，构成了一种求解超弹性动力学的新型迭代方法。我们通过与SIMPLE预处理器和一级区域分解预处理器进行比较，证明了所提出的预处理技术的有效性。研究了两个代表性例子：各向同性超弹性立方体的压缩和完全不可压缩各向异性超弹性动脉壁模型的拉伸试验。检验了预处理技术在材料特性方面的稳健性和并行性能。
