CV circular-arc ordinary and (multi-) wedge elements for harmonic problems

The computational advantages of the complex variable (CV) are employed to derive recurrence quadrature rules and to develop robust subroutines for circular-arc boundary elements, both ordinary and singular. The elements provide (i) accurate approximation of the geometry of boundaries and contacts and (ii) accurate approximation of physical quantities along an element. The first, geometrical, gain is due to the fact that circular-arc approximation allows one to have a continuous tangent at the common points of neighbouring elements at smooth parts of a curve. The second, density approximation, gain is due to using trigonometric polynomials multiplied when appropriated by functions accounting for the asymptotic behaviour of a physical quantity. We focus on integrals containing the log-type kernels and real density. These integrals are of special need when influxes of heat, fluid, electricity or particle concentration to highly conductive contacts are considered. Other integrals, although involving complications when the density is real, are easily evaluated by properly adjusting the already-known technique. Numerical results illustrate the accuracy, specific features and potential of the developed CV boundary elements.