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A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning. (arXiv:1809.06350v1 [math.NA])
来源于:arXiv
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
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