AN OBJECT-ORIENTED CLASS DESIGN FOR THE GENERALIZED FINITE ELEMENT METHOD PROGRAMMING

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DORIVAL PIEDADE NETO
MANOEL DêNIS COSTA FERREIRA
SERGIO PERSIVAL BARONCINI PROENçA

Abstract

THE GENERALIZED FINITE ELEMENT METHOD (GFEM) IS A NUMERICAL METHOD BASED ON THE FINITE ELEMENT METHOD (FEM), PRESENTING AS ITS MAIN FEATURE THE POSSIBILITY OF IMPROVING THE SOLUTION BY MEANS OF LOCAL ENRICHMENT FUNCTIONS. IN SPITE OF ITS ADVANTAGES, THEMETHOD DEMANDS A COMPLEX DATA STRUCTURE, WHICH CAN BE ESPECIALLY BENEFITED BY THE OBJECT-ORIENTED PROGRAMMING (OOP). EVEN THOUGH THE OOP FOR THE TRADITIONAL FEM HAS BEEN EXTENSIVELY DESCRIBED IN THE TECHNICAL LITERATURE, SPECIFIC DESIGN ISSUES RELATEDTO THE GFEM ARE YET LITTLE DISCUSSED AND NOT CLEARLY DEFINED. IN THE PRESENT ARTICLE IT IS DESCRIBED AN OBJECT-ORIENTED (OO) CLASS DESIGN FOR THE GFEM, AIMING TO ACHIEVE A COMPUTATIONAL CODE THAT PRESENTS A FLEXIBLE CLASS STRUCTURE, CIRCUMVENTING THE DIFFICULTIES ASSOCIATED TO THE METHOD CHARACTERISTICS. THE PROPOSED DESIGNIS EVALUATED BY MEANS OF SOME NUMERICAL EXAMPLES, COMPUTED USING A CODE IMPLEMENTED IN PYTHON PROGRAMMING LANGUAGE. ONE CONCLUDES THAT THE OO DESIGN FULFILLS THE AIMED PURPOSE.

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