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Scalable TFETI with optional preconditioning by conjugate projector for transient frictionless contact problems of elasticity. (English) Zbl 1352.74345

Summary: The FETI based domain decomposition method is adapted to implement the time step of the Newmark scheme for the solution of dynamic contact problems without friction. If the ratio of the decomposition and discretization parameters is kept uniformly bounded, then the cost of the time step is proved to be proportional to the number of nodal variables. The algorithm uses our in a sense optimal MPRGP algorithm for the solution of strictly convex bound constrained quadratic programming problems with optional preconditioning by the conjugate projector to the subspace defined by the trace of the rigid body motions on the artificial subdomain interfaces. The proof of optimality combines the convergence theory of our MPRGP algorithm, the classical bounds on the spectrum of the mass and stiffness matrices, and our theory of the preconditioning by a conjugate projector for nonlinear problems. The results are confirmed by numerical solution of 2D and 3D dynamic contact problems.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
90C20 Quadratic programming

Software:

MatSol; Total FETI
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Full Text: DOI

References:

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