Analytical and adaptive numerical evaluation of all terms required in a 3D boundary element implementations for potential problems using linear triangle elements

Resumo

The present contribution introduces a formulation for 3D steady-state potential and elastostatics prob-
lems that ends up with the analytical handling of all integrals necessary in an implementation using linear triangle

(T3) elements – whether regular, improper, quasi-singular, singular or hypersingular integrals are involved. The
boundary element matrices – including the discontinuous term of the double-layer potential matrix – are obtained
in a straightforward way with the use of analytically pre-evaluated integrals. Results at internal points that may
be located arbitrarily close to the boundary are also given analytically. The paper describes the main concepts and
computational features of the proposed formulation and presents an example of 3D potential problem to illustrate
the most challenging topological configurations one might deal with in practical applications. For source points
sufficiently far from a boundary element an adaptive numerical integration scheme is also proposed for the sake of
computational speed – and how far a point should be in order to be considered far is also discussed.