Analysis of high order approximations by spectral interpolation applied to the Boundary Element Method in elastostatics

Renério Pereira Neto¹; Fabio Carlos da Rocha¹; Aref Kalilo Lima Kzam²

¹ Federal University of Sergipe; ² Federal University of Latin American Integration

doi:10.20906/CPS/CILAMCE2017-0610

Resumo

In the direct formulation of the boundary element method, significant numerical errors can occur when trying to reproduce a complex geometry accurately. The polynomial interpolation and the order of the approximations employed influence these errors which affect the physical solution of the problem. This work presents a comparative study between the equidistant nodes approach and the spectral base applied in the analysis of two-dimensional elastostatic problems by boundary element method. High order approximations are used to verify the method's conditioning. Based on the evaluation of the Lebesgue constant, a convergence analysis is carried out by means of the quantification of the phenomenon caused by the use of the high order polynomials called the Runge phenomenon. Examples are evaluated and improvements of the results are verified by using a spectral interpolation.

Palavras-chave: Boundary Element Method in elastostatic; Equidistant nodes; Spectral nodes; Runge phenomenon; Lebesgue constant