Genetic algorithms with Nelder-Mead optimization for the finite elements methods applied on non-linear problems in fluid mechanics

Authors:
Nikos E. Mastorakis
Affiliations:
WSEAS Research Department, Zografou, Athens, Greece and Technical University of Sofia, English Language Faculty, Industrial Engineering Department, Sofia, Bulgaria and Military Institutes of Unive ...
Venue:
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Year:
2009

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Abstract

The p-Laplacian operator, or the p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. The p-Laplacian equation is a generalization of the PDE of Laplace Equation and in this paper, we present a way of its solution using Finite Elements. Our method of Finite Elements leads to an Optimization Problem that can be solved by an appropriate combination of Genetic Algorithms and Nelder- Mead. Our method is illustrated by a numerical example. Other methods for the solution of other equations that contain the p-Laplacian operator are also discussed.