IMPOSITION OF DIRICHLET BOUNDARY CONDITIONS IN ELEMENT FREE GALERKIN METHOD THROUGH AN OBJECT-ORIENTED IMPLEMENTATION

Authors

  • SAMIRA HOSSEINI FEDERAL UNIVERSITY OF MINAS GERAIS
  • MOHAMMAD MALEKAN FEDERAL UNIVERSITY OF MINAS GERAIS
  • ROQUE LUIS DA SILVA PITANGUEIRA FEDERAL UNIVERSITY OF MINAS GERAIS
  • RAMON PEREIRA SILVA FEDERAL UNIVERSITY OF MINAS GERAIS

Keywords:

ELEMENT FREE GALERKIN METHOD, EFG-FE COUPLING, LAGRANGE MULTIPLI-ERS, PENALTY METHOD, OBJECT-ORIENTED PROGRAMMING

Abstract

ONE OF THE MAIN DRAWBACKS OF ELEMENT FREE GALERKIN (EFG) METHOD IS ITS DEPENDENCE ON MOVING LEAST SQUARE SHAPE FUNCTIONS WHICH DON’T SATISFY THE KRONECKER DELTA PROPERTY, SO IN THIS METHOD IT’S NOT POSSIBLE TO APPLY DIRICHLET BOUNDARY CONDITIONS DIRECTLY. THE AIM OF THE PRESENT PAPER IS TO DISCUSS DIFFERENT ASPECTS OF THREE WIDELY USED METHODS OF APPLYING DIRICHLET BOUNDARY CONDITIONS IN EFG METHOD, CALLED LAGRANGE MULTIPLIERS, PENALTY METHOD, AND COUPLING WITH FINITE ELEMENT METHOD. NUMERICAL SIMULATIONS ARE PRESENTED TO COMPARE THE RESULTS OF THESE METHODS FORM THE PERSPECTIVE OF ACCURACY, CONVERGENCE AND COMPUTATIONAL EXPENSE. THESE METHODS HAVE BEEN IMPLEMENTED IN AN OBJECT-ORIENTED PROGRAMING ENVIRON-MENT, CALLED INSANE, AND THE RESULTS ARE PRESENTED AND COMPARED WITH THE ANALYTICAL SOLUTIONS.

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Published

2017-04-20

Issue

Vol. 14 No. 06 (2017)

Section

Articles

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