Contour-integral representation of single and double layer potentials for axisymmetric problems

Based on recently proposed non-singular contour-integral representations of single and double layer potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular layer potentials in terms of elliptic integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the double layer potential. The results are compared with another method for calculating the single and double layer potentials. The comparison demonstrates a higher accuracy and better performance of the presented formulas

Contour-integral representation of single and double layer potentials for axisymmetric problems

Based on recently proposed non-singular contour-integral representations of single and double layer potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular layer potentials in terms of elliptic integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the double layer potential. The results are compared with another method for calculating the single and double layer potentials. The comparison demonstrates a higher accuracy and better performance of the presented formulas