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Development of a genetic algorithm‐based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems
Author(s) -
BaniHani Suleiman,
De Suvranu
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1678
Subject(s) - lookup table , finite element method , computation , algorithm , gaussian , numerical integration , table (database) , reduction (mathematics) , genetic algorithm , computer science , gaussian quadrature , adaptive quadrature , spheres , mathematics , mathematical optimization , geometry , mathematical analysis , artificial intelligence , structural engineering , nyström method , physics , engineering , data mining , boundary value problem , control (management) , quantum mechanics , control theory (sociology) , programming language , astronomy
It is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure. Copyright © 2006 John Wiley & Sons, Ltd.