Fast capacitance computation using three-dimensional second-kind integral equation and AIM

Capacitance extraction based on the integral equation has become popular. Several fast algorithms have been developed to reduce the computational complexity and memory requirement. One powerful method is the adaptive integral method (AIM) developed by Bleszynski et al. (1996). We apply the AIM to solve the second-kind integral equation that can be used to calculate the capacitance matrix for an arbitrarily shaped 3D structure. The uniformity of the multipole moment approximation of the second-kind integral equation is revealed theoretically and numerically, that can guarantee the accuracy of AIM for capacitance computation of any structure. Numerical experiments demonstrate that the memory requirement and computational complexity of present method can be nearly reduced to O(N) and O(NlogN) for 3D problems, respectively. Furthermore, the employment of the second-kind integral equation significantly improves the efficiency of the AIM by reducing the number of iterations for convergence.