Optimal with respect to accuracy algorithms for calculation of multidimensional weakly singular integrals and applications to calculation of capacitances of conductors of arbitrary shapes (Q1417647)

The detailed algorithms, asymptotically optimal with respect to accuracy and to complexity, for calculating hypersingular integrals, the Poisson and Cauchy type integrals, and multidimensional Cauchy type integrals are presented. The cubature formulas are adapted for calculating weakly singular integrals on Lyapunov surfaces. The goal is the calculation of capacitances and polarizability tensors of bodies of arbitrary shapes. Numerical tests are performed on the example of calculation of capacitances of various ellipsoids, the analytical formulas being known in these cases.