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

Mark Ainsworth; L. Angela Mihai

Applications of Mathematics (2006)

  • Volume: 51, Issue: 2, page 93-128
  • ISSN: 0862-7940

Abstract

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We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised 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.

How to cite

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Ainsworth, Mark, and Mihai, L. Angela. "A comparison of solvers for linear complementarity problems arising from large-scale masonry structures." Applications of Mathematics 51.2 (2006): 93-128. <http://eudml.org/doc/33247>.

@article{Ainsworth2006,
abstract = {We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised 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.},
author = {Ainsworth, Mark, Mihai, L. Angela},
journal = {Applications of Mathematics},
keywords = {linear elasticity; equilibrium problems; variational inequality; complementarity problems; masonry structures; linear elasticity; equilibrium problems; variational inequality; complementarity problems; masonry structures},
language = {eng},
number = {2},
pages = {93-128},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A comparison of solvers for linear complementarity problems arising from large-scale masonry structures},
url = {http://eudml.org/doc/33247},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Ainsworth, Mark
AU - Mihai, L. Angela
TI - A comparison of solvers for linear complementarity problems arising from large-scale masonry structures
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 93
EP - 128
AB - We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised 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.
LA - eng
KW - linear elasticity; equilibrium problems; variational inequality; complementarity problems; masonry structures; linear elasticity; equilibrium problems; variational inequality; complementarity problems; masonry structures
UR - http://eudml.org/doc/33247
ER -

References

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  1. Nonnegative Matrices in the Mathematical Sciences. Computer Science and Scientific Computing Series, Academic Press, New York, 1979. (1979) MR0544666
  2. 10.1007/978-1-4757-4338-8_7, Springer-Verlag, New York, 1994. (1994) MR1278258DOI10.1007/978-1-4757-4338-8_7
  3. Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften, Vol. 219, Springer-Verlag, Berlin-Heidelberg-New York, 1976. (1976) MR0521262
  4. Encyclopedia of physics, Existence Theorems in Elasticity-Boundary Value Problems of Elasticity with Unilateral Constraints, Volume  VI  a/2, S. Flügge (ed.), Springer-Verlag, Berlin, 1972, pp. 347–427. (1972) 
  5. Practical Optimization, Academic Press, London, 1981. (1981) MR0634376
  6. Numerical Analysis of Variational Inequalities. Studies in Mathematics and its Applications, Vol.  8, North-Holland, Amsterdam-New York-Oxford, 1981, English version edition. (1981) MR0635927
  7. 10.1287/opre.15.3.482, Oper. Res. 15 (1967), 482–494. (1967) Zbl0154.19604MR0211756DOI10.1287/opre.15.3.482
  8. The primal-dual active set strategy as a semismooth Newton method, SIAM J.  Optim. 13 (2003), 865–888. (2003) MR1972219
  9. 10.1093/imamat/69.1.1, IMA  J.  Appl. Math. 69 (2004), 1–26. (2004) MR2029355DOI10.1093/imamat/69.1.1
  10. 10.1002/num.20053, Numer. Methods Partial Differential Equations 21 (2005), 586–610. (2005) MR2128598DOI10.1002/num.20053
  11. Solution of Variational Inequalities in Mechanics. Applied Mathematical Sciences, Vol. 66, Springer-Verlag, Berlin-Heidelberg-New York, 1988. (1988) MR0952855
  12. 10.1016/S0378-4754(01)00433-5, Math. Comput. Simul. 60 (2002), 1–17. (2002) MR1916897DOI10.1016/S0378-4754(01)00433-5
  13. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. Studies in Applied Mathematics, Vol. 8, SIAM, Philadelphia, 1988. (1988) MR0961258
  14. Solving Least Squares Problems. Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, 1974. (1974) MR0366019
  15. Complementarity, Linear and Nonlinear Programming, Heldermann-Verlag, Berlin, 1988. (1988) Zbl0634.90037MR0949214
  16. 10.1090/S0025-5718-1994-1250776-4, Math. Comput. 63 (1994), 625–643. (1994) MR1250776DOI10.1090/S0025-5718-1994-1250776-4
  17. Problems and Theorems in Linear Algebra. Translations of Mathematical Monographs, Vol.  134, AMS, Providence, 1994. (1994) MR1277174
  18. Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1997. (1997) Zbl0863.65031MR1422257

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