A finite difference approach to solve obstacle-type problems using complementarity models

Authors

  • Daniel A. Gutierrez Pachas
  • Miguel Cutipa Coaquira

DOI:

https://doi.org/10.5540/03.2022.009.01.0230

Keywords:

Finite difference method, Complementarity models, obstacle problems.

Abstract

This paper focuses on elaborating practical finite difference schemes to reduce the computational cost incurred in the construction of large sparse matrices. Our methodology generates a sequence of lower-dimensional vectors to mitigate this cost. In addition, we test our approach on obstacle-type problems in its equivalent version of a complementarity model.

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Author Biographies

Daniel A. Gutierrez Pachas

Department of Computer Science, Universidad Católica San Pablo, Arequipa, Peru.

 

Miguel Cutipa Coaquira

Facultad de Ingeniería Industrial y de Sistemas, Universidad Nacional de Ingeniería, Lima, Peru.

References

Randall J LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. 2007.

J.-F. Rodrigues. “Obstacle problems in mathematical physics”. In: North-Holland mathematics studies 134 (1987).

Michael C Ferris and Jong-Shi Pang. “Engineering and economic applications of complementarity problems”. In: Siam Review 39.4 (1997), pp. 669–713.

Daniel A. Gutierrez-Pachas. “Inequações variacionais e aplicações em problemas tipo obstáculo com resolução numérica via complementaridade”. Master dissertation. Universidade Federal de Juiz de Fora, 2013.

Angel ER Gutierrez et al. “An interior point algorithm for mixed complementarity nonlinear problems”. In: Journal of Optimization Theory and Applications 175.2 (2017), pp. 432– 449.

Olvi L Mangasarian. “Equivalence of the complementarity problem to a system of nonlinear equations”. In: SIAM Journal on Applied Mathematics 31.1 (1976), pp. 89–92.

Carl Geiger and Christian Kanzow. “On the resolution of monotone complementarity problems”. In: Computational Optimization and Applications 5.2 (1996), pp. 155–173.

José Herskovits and Sandro R. Mazorche. “A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics”. In: Structural and Multidisciplinary Optimization 37 (2009), pp. 435–446.

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Published

2022-12-08

Issue

Section

Trabalhos Completos