Yu. V. Khalevitsky, A. V. Konovalov, A. S. Partin

CONVERGENCE PATTERNS OF KRYLOV SUBSPACE SOLVERS IN THE SIMULATION OF LARGE ELASTIC-PLASTIC DEFORMATIONS OF HETEROPHASE MEDIA

Simulating the process of heterophase medium deformation is essential for the scientific substantiation of composite material forming. Representative-volume models of composite materials are generally represented as a conglomerate of elastic and elastic-plastic bodies. Usually, composite deformations are numerically simulated by the finite element method, which requires solving a series of simultaneous linear equations. When applying a fine mesh, an iterative Krylov subspace solver is usually used.

We present a comparison of convergence for several iterative solvers in a two-dimensional finite-element model problem on the deformation of a heterophase representative volume of a composite. The volume contains 13,000 three-node triangular finite elements. The composite is based on the AMg6 alloy, and it contains 10 vol% of silicon carbide reinforcement.

Six methods are compared within the scope of the article: the biconjugate gradient stabilized method (BiCGStab), the generalized minimal residual method (GMRES), the conjugate gradient squared method (CGS), the quasi minimal residual method (QMR) and variants of the BiCGStab and QMR methods, namely BiCGStab(L) and TFQMR. The best timing is shown by a relatively rare QMR method.

Acknowledgments: The work was supported from the federal budget (government registration No. АААА-А18-118020790140-5) in terms of studying linear solver convergence in elastoplastic problems and partially supported by the Russian Science Foundation (Project 14-19-01358) in the part of developing a finite element suite for simulating composite structure deformation.

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