Capacitance extraction for three-dimensional (3-D) conductors located on planar structures has various applications, especially in the design and packaging of integrated circuits. One of the most commonly used methods for capacitance extraction problems is the method of moments (MM). In this study, the forward-backward (FB) method, which is an iterative MM, is applied for solving these problems effectively. It is found that the method is an O(N/sup 2/) algorithm per iteration, where N is the total number of unknowns. In addition, the FB method provides accurate results compared to those of the standard MM with less computational times for relatively large problems. Convergence characteristics of the FB method are also studied in this paper.
A new technique called "forward-backward," has been developed for solving the magnetic field integral equation (MFIE) for perfectly conducting azimuthally homogeneous surfaces, including cases where the incident radiation has a lowgrazing angle. The technique involves splitting both the surface current and the MFIE into two pieces; one representing primarily forwardly scattered energy and one representing primarily backwardly scattered energy. Each of the new integral equations can be solved by an iterative stepping procedure. The technique is applied to two sample problems–the classic Sommerfeld wedge and a peaked surface consisting of two filtered exponentials. The obtained solutions are shown to be accurate for each of these problems.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.