A TFETI Domain Decomposition Solver for Elastoplastic Problems. We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an associated elastoplastic model with the von Mises plastic criterion and the linear isotropic hardening law. Such a model is discretized by the implicit Euler method in time and the consequent one time step elastoplastic problem by the finite element method in space. The latter results in a system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI domain decomposition method. The proposed TFETI based algorithm was implemented in Matlab parallel environment and its performance was illustrated on a 3D elastoplastic benchmark. Numerical results for different time discretizations and mesh levels are presented and discussed and a local quadratic convergence of the semismooth Newton method is observed.
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References in zbMATH (referenced in 9 articles )
Showing results 1 to 9 of 9.
- Čermák, M.; Sysala, S.; Valdman, J.: Efficient and flexible Matlab implementation of 2D and 3D elastoplastic problems (2019)
- Čermák, Martin; Hapla, Václav; Kružík, Jakub; Markopoulos, Alexandros; Vašatová, Alena: Comparison of different FETI preconditioners for elastoplasticity (2017)
- Vašatová, Alena; Tomčala, Jiří; Sojka, Radim; Pecha, Marek; Kružík, Jakub; Horák, David; Hapla, Václav; Čermák, Martin: Parallel strategies for solving the FETI coarse problem in the PERMON toolbox. (2017)
- Kanno, Yoshihiro: A fast first-order optimization approach to elastoplastic analysis of skeletal structures (2016)
- Roubíček, Tomáš; Valdman, Jan: Perfect plasticity with damage and healing at small strains, its modeling, analysis, and computer implementation (2016)
- Axelsson, Owe; Sysala, Stanislav: Continuation Newton methods (2015)
- Cermak, M.; Haslinger, J.; Kozubek, T.; Sysala, S.: Discretization and numerical realization of contact problems for elastic-perfectly plastic bodies. II: Numerical realization, limit analysis (2015)
- Markopoulos, Alexandros; Hapla, Vaclav; Cermak, Martin; Fusek, Martin: Massively parallel solution of elastoplasticity problems with tens of millions of unknowns using permoncube and FLLOP packages (2015)
- Čermák, M.; Kozubek, T.; Sysala, S.; Valdman, J.: A TFETI domain decomposition solver for elastoplastic problems (2014)