Analytical computation of impedance integrals with power-law Green´s functions

In this contribution, a method is presented for reducing the number of subsequent integrations that occur in impedance integrals with Green´s functions of the form R^ν, with R the distance between source and observation point. The method allows the number of integrations to be reduced to 1 in the two dimensional case and 2 in the three dimensional case, irrespective of the number of subsequent integrations that were originally present. These last integrations can be done analytically using well-known results if ν ϵ Z, resulting in a computation that is free of numerical integrations. The dynamic Green´s function can be treated in a semi-analytical way, by expanding it into a Taylor series in the wavenumber. The method can be applied if both the basis and test functions are polynomial functions with polygonal support and if certain non-parallelity conditions are satisfied.