Numerical quadrature for the approximation of singular oscillating integrals appearing in boundary integral equations

摘要

Boundary Integral Equation formulations can beused to describe electromagnetic shielding problems. Yet, thisapproach frequently leads to integrals which contain a singularityand an oscillating part. Those integrals are difficult to handlewhen integrated naivly using standard integration techniques, andin some cases even a very high number of integration nodes willnot lead to precise results.We present a method for the numerical quadrature of an integralwith a logarithmic singularity and a cosine oscillator: a modifiedFilon-Lobatto quadrature for the oscillating parts and an integraltransformation based on the error function for the singularity.Since this integral can be solved analytically, we are in aposition to verify the results of our investigations, with a focuson precision and computation time.