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

TL;DR

This paper introduces a new iterative method with nested block preconditioning for hyper-elastodynamics, improving robustness and efficiency in solving complex continuum mechanics problems.

Contribution

The paper presents a novel nested block preconditioning technique combined with Krylov methods for hyper-elastodynamics, enhancing solver robustness and computational efficiency.

Findings

The proposed method outperforms traditional preconditioners like SIMPLE.

It demonstrates robustness across different material properties.

Parallel performance is effectively maintained.

Abstract

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. 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.