The quark core of baryons can be described with the help of the numer-ical solution of the Poincare covariant Faddeev equation. Hereby the usedinput as e.g. the quark propagator are taken from non-perturbative stud-ies of Landau gauge QCD. Within this framework, the bound state of thenucleon, expressed in terms of its wave- and vertex functions, emerges as asolution of a homogeneous Bethe-Salpeter equation, which is in practiceobtained using an iterative eigenvalue solver. In order to control and con-sequently optimise the numerical error, automatic integration algorithmsbased upon interpolating quadrature formulae of Gauss type and the errorestimations derived from their corresponding Kronrod extensions are in-troduced and their application with respect to the integration of quantitiesin the complex plane is studied. Using the established serial algorithm forthe iterative solution strategy, different approaches towards the computa-tion of the solution in a distributed fashion are introduced and developedusing communication patterns from the Message Passing Interface (MPI)standard. In passing, the necessary terminologies and metrics to gaugenumerical efficiency in a parallel environment is provided. The impact ofthe numerical optimisation with respect to the resulting wave functionsand nucleon mass is outlined.