Development of Bartky´s quadrature formulae and applications in BEM analysis

A new accurate and efficient algorithm for the integration of a special class of periodic functions is introduced. Fixed order and optimum order formulae which are based on Bartky´s transformation are developed. The nodes and weights of the quadrature can be easily computed and no storage is necessary. The algorithm permits a check on the accuracy of the integration by increasing the order of the quadratures and can be used for the efficient integration of the various fundamental solutions encountered in the BEM analysis of geometries with rotational symmetry. Numerical results are presented for smooth and non-smooth functions to compare the performance of Bartky´s quadrature with that of the other commonly used methods. The results show that as compared with Simpson´s rule, the new quadrature can reduce the number of nodes required for a given accuracy by a factor of O(10³).