Collision of an obstacle by an elastic bar in a gravity field: solution with discontinuous velocity and space-time primal-dual active set algorithm

Collision of an obstacle by an elastic bar in a gravity field: solution with discontinuous velocity and space-time primal-dual active set algorithm Full article

Journal

Algorithms
ISSN: 1999-4893

Output data

Year: 2026, Volume: 19, Number: 1, Article number : 88, Pages count : DOI: 10.3390/a19010088

Tags

mpact contact dynamics; variational inequality; discontinuous velocity; space-time finite element; primal-dual active set

Authors

Kovtunenko Victor Anatolʹevich ^1,2

Affiliations

1	Siberian Division of the Russian Academy of Sciences, Lavrentyev Institute of Hydrodynamics, Novosibirsk 630090, Russia
2	Department of Mathematics and Scientific Computing, Karl-Franzens University of Graz

A class of one-dimensional dynamic impact models is investigated with respect to nonsmooth velocities using variational inequalities and space-time finite element approximation. For the problem of collision of a rigid obstacle by an elastic bar in the gravitational field, a benchmark based on particular solutions to the wave equation is constructed on a partition of rectangle domains. The full discretization of the collision problem is carried out over a uniform space-time triangulation and extended to distorted meshes. For the solution of the corresponding variational inequality, a semi-smooth Newton-based primal-dual active set algorithm is applied. Numerical experiments demonstrate advantages over timestep approximation: a high-precision numerical solution is computed in a few iterations without any spurious oscillations.

Kovtunenko V.A.
Collision of an obstacle by an elastic bar in a gravity field: solution with discontinuous velocity and space-time primal-dual active set algorithm
Algorithms. 2026. V.19. N1. 88 . DOI: 10.3390/a19010088 OpenAlex

OpenAlex:

W7124848019

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