COBEM99

S25 Métodos Numéricos

Title:

POINT DOMAIN METHOD AND APPLICATIONS FOR 2-DIMENSIONAL POISSON PROBLEMS

Summary :

ABSTRACT: THE 2-DIMENSIONAL VERSION OF THE POINT DOMAIN METHOD (PDM) IS PRESENTED AND APPLIED TO THE SOLUTION OF CLASSICAL POISSON PROBLEMS. IT CONSISTS OF A LINEAR ALGEBRA OPERATOR BASED ON APPROXIMATION FIELDS WHICH ASSURES CONTINUITY OF THE HIGHER ORDER DERIVATIVES FOR THE NUMERICAL SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS. THE MAIN TOPICS ABOUT THE PROPOSED METHOD ARE DISCUSSED: SYSTEMATIC METHODOLOGY FOR DEVELOPMENT OF THE PDM FUNCTIONS, MESHLESS DISCRETIZATION AND NON-DEPENDENCY OF A SPECIFIC DIFFERENTIAL EQUATION. DIFFERENT BOUNDARY VALUED PROBLEMS CONCERNING POISSON EQUATION ARE ANALYSED. A TEST PROBLEM IS PROPOSED AND CONSIDERATIONS ABOUT POINT DOMAIN METHOD AND DUAL RECIPROCITY METHOD (DRM) SOLUTIONS BASED ON THE SAME ORDER OF THE LINEAR SYSTEMS ARE PRESENTED. THE PDM IS ALSO USED FOR THE SOLUTION OF TORSION PROBLEMS IN THE THEORY OF ELASTICITY. THE CASES OF TRIANGULAR, RECTANGULAR AND RECTANGULAR CRACKED CROSS SECTIONS ARE STUDIED AND COMPARED WITH KNOWN RESULTS FROM THE LITERATURE. KEYWORDS: COMPUTATIONAL METHODS, DIFFERENTIAL EQUATIONS, HIGH ORDER APPROXIMATIONS

Author :

Iguti, Fernando 0
Neto, Euclides Mesquita
Neto, Alessandro Teixeira
Nogueira Jr., Alberto Costa

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