On a simple code for the accurate evaluation of integrals in the 2D boundary element method using arbitrarily high order, curved elements

Ney Augusto Dumont¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/CILAMCE2017-1277

Resumo

This paper is the sequel of an article recently prepared, in which is shown that the traditional, collocation boundary element method (BEM) may undergo two decisive conceptual improvements for a generally curved boundary: (1) the interpolation function for normal fluxes or traction forces (for potential or elasticity problems) is redefined, and (2) only Gauss-Legendre quadrature turns out to be required. In the present paper, a simple, unified code is outlined for the arbitrarily highly accurate evaluation of the constituent matrices of 2D problems as well as of results at internal points independently from how convoluted a problem's topology may be (but given the representation limitations of a discretization mesh). A collateral, but not less relevant, outcome of the proposed developments is that regularization methods, special quadrature schemes and so many methods that intend to conceptually deviate from the originally stated BEM as an attempt to offer numerical improvements turn out to be mostly just misconceptions. A few numerical examples illustrate the high numerical accuracy one may arrive at in the frame of the present formulation.

Palavras-chave: Boundary elements; Numerical singularities; Numerical quasi singularities