Fast Capacitance Computation Based On Adaptive Integral Solution of Second-Kind Integral Equation

Abstract

Standard approach to calculate electrostatic force and capacitance by solving first-kind integral equation will lead to ill-conditioned linear system. The condition number of resultant discretization matrix can be improved by employing the second-kind integral equation. Adaptive integral method (AIM) is applied in this paper to solve the second-kind integral equation that can be used to calculate capacitance coefficients for three-dimensional structures. The uniformity of multipole moment approximation of the second-kind integral equation is revealed theoretically and numerically; it is realized that the present approach can guarantee the accuracy of AIM for computing capacitance of any structure. The numerical experiments demonstrate that the memory requirement and computational complexity of the present method can be reduced to O(N) and O(N log N) for three-dimensional static problems, respectively. Furthermore, the employment of the second-kind integral equation significantly improves the efficiency of AIM by reducing the number of iterations for convergence.