Rigorous approach to analysis of 2-D electrostatic-field problems for multi-conductor systems

The two-dimensional N-body potential problem is rigorously solved with emphasis on electrostatics. By the Method of Analytical Regularization, the solution is obtained from N coupled second kind infinite systems of linear algebraic equations that are effectively solved numerically by a truncation method. A combination of the fast convergence with fast and accurate computation of the matrix elements, based on the Fast Fourier Transform, makes the computational routine extremely efficient: in most cases the computational time measures a few seconds. As an example, the developed algorithm is applied to a calculation of the capacitance matrix for N arbitrary profiled charged cylinders in a space surrounded by a grounded cylindrical shield.