Complex-variable, high-precision formulation of the consistent boundary element method for 2D potential and elasticity problems

The collocation boundary element method was recently entirely revisited on the basis of a consistent derivation of Somigliana's identity in terms of weighted residuals. Both conceptually , for the sake of code implementation, the correct traction force interpolation along generally curved boundaries, as for elasticity problems, leads to the enunciation of an inedited, actually long-sought, convergence theorem as well as to considerable numerical simplifications. Numerical evaluations for two-dimensional problems require exclusively Gauss-Legendre quadrature plus eventual correction terms obtained analytically regardless of the order or shape of the implemented boundary element interpolation. Arbitrarily high precision and accuracy is achievable for low-cost computation, as eventual mesh-subdivision refinements should take place only if the mechanical simulation demands - and not just for numerical evaluations. We now show that considerable simplification is obtained by switching the formulation from real to complex variable. Precision, round-off errors , accuracy of a given numerical implementation may be kept - identifiably and separately - under control, as assessed for some potential and elasticity examples with extremely challenging topologies. In fact, source-field distances may be arbitrarily small - far smaller than deemed feasible in continuum mechanics, as we resort to nothing else than the problem's mathematics.