A comparison of solvers for linear complementarity problems arising from large-scale masonry structures.

*(English)*Zbl 1164.74355Summary: We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretization of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretized using piecewise quadratic finite elements on a triangulation of the domain. At the discrete level, the variational inequality is reformulated as a classical linear complementarity system. We compare several state-of-art algorithms that have been advocated for such problems. Computational tests illustrate the use of these methods for a large collection of elastic bodies, such as a simplified bidimensional wall made of bricks or stone blocks, deformed under volume and surface forces.

##### MSC:

74B10 | Linear elasticity with initial stresses |

74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |

49J40 | Variational inequalities |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

##### Keywords:

linear elasticity; equilibrium problems; variational inequality; complementarity problems; masonry structures
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\textit{M. Ainsworth} and \textit{L. A. Mihai}, Appl. Math., Praha 51, No. 2, 93--128 (2006; Zbl 1164.74355)

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