Space-time primal-dual active set method: benchmark for collision of elastic bar with discontinuous velocity

Space-time primal-dual active set method: benchmark for collision of elastic bar with discontinuous velocity Full article

Journal

Computation
ISSN: 2079-3197

Output data

Year: 2025, Volume: 13, Number: 9, Article number : 210, Pages count : 15 DOI: 10.3390/computation13090210

Tags

impact contact dynamics, variational inequality, discontinuous velocity, space-time finite element, primal-dual active set

Authors

Kovtunenko Victor Anatolʹevich ^1,2

Affiliations

1	Lavrentyev Institute of Hydrodynamics
2	University of Graz

The dynamic contact problem describing collision of an elastic bar with a rigid obstacle, prescribed by an initial velocity, is considered in a variational formulation. The non-smooth, piecewise-linear solution is constructed analytically using partition of a 2D rectangular domain along characteristics. Challenged by the discontinuous velocity after collision, full discretization of the problem is applied that is based on a space-time finite element method. For an iterative solution of the discrete variational inequality, a primal–dual active set algorithm is used. Computer simulation of the collision problem is presented on uniform triangle grids. The active sets defined in the 2D space-time domain converge in a few iterations after re-initialization. The benchmark solution at grid points is indistinguishable from the analytical solution. The discrete energy has no dissipation, it is free of spurious oscillations, and it converges super-linearly under mesh refinement.

Kovtunenko V.A.
Space-time primal-dual active set method: benchmark for collision of elastic bar with discontinuous velocity
Computation. 2025. V.13. N9. 210 :1-15. DOI: 10.3390/computation13090210 РИНЦ OpenAlex

Submitted:	Jul 31, 2025
Accepted:	Aug 18, 2025
Published print:	Sep 1, 2025

Elibrary:	82810644
OpenAlex:	W4413893546

Пока нет цитирований