Space-time primal-dual active set method: benchmark for collision of elastic bar with discontinuous velocity Full article
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Computation
ISSN: 2079-3197 |
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| 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 | ||||
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Abstract:
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.
Cite:
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 WOS Scopus РИНЦ OpenAlex
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 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 31, 2025 |
| Accepted: | Aug 18, 2025 |
| Published print: | Sep 1, 2025 |
Identifiers:
| Web of science: | WOS:001579585900001 |
| Scopus: | 2-s2.0-105017067009 |
| Elibrary: | 82810644 |
| OpenAlex: | W4413893546 |