A TFETI Domain Decomposition Solver for Elastoplastic Problems
It provides an efficient parallel solver for nonlinear elastoplastic problems, but the contribution is incremental as it applies existing TFETI and Newton methods to a specific material model.
The paper proposes a parallel TFETI domain decomposition solver for elastoplastic problems with hardening, achieving local quadratic convergence of the semismooth Newton method on a 3D benchmark.
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.