Efficient machine precision computation of impedance matrix elements in surface integral equation formulations

The direct evaluation program tailored to the singular integrals arising in the first-kind and second-kind Fredholm surface integral equation formulations is presented. The exponential convergence of the proposed technique can safely guarantee the inherited asymptotic accuracy of Galerkin discretization schemes. In this contribution, we highlight the key-features of the direct evaluation method and discuss some critical points regarding its efficient and automatic implementation in modern programming platforms. Numerical results demonstrate that the uncertainty about the accuracy of the associated impedance matrix elements is removed, allowing a safe shift of future research studies on other aspects of surface integral equation formulations.