Fast Capacitance Extraction for Finite Planar Periodic Structures Using the Generalized Forward-Backward and Novel Spectral Acceleration Method

Abstract

Abstract-The generalized forward-backward and novel spectral acceleration (GFB/NSA) method is applied to capacitance extraction problems of finite planar periodic structures. In the GFB method, the interaction within a unit cell can be calculated and stored beforehand. The interactions between relatively far-separated unit cells are however calculated by the GFB/NSA method to further accelerate the calculation speed. The contributions to a receiving element on finite planar periodic structures are separated into weak and strong source contributions by an appropriate separation index, which is conveniently specified by an amount of unit cells rather than a distance. The strong source contribution is performed by the standard matrix-vector multiplication in the GFB method, while the weak source contribution is computed using the NSA algorithm. Numerical examples show comparisons of the GFB/NSA method with a commercial software, including the efficiency of the method. With the array increment in one direction, the GFB/NSA method shows O(N ) in the calculation time per iteration, while its memory requirement for a very large problem also tends to be O(N ), where N is the number of unknowns.

Forward‐backward method with a spectral acceleration algorithm for capacitance extraction of planar structures on a single‐layered medium

“…and The Green's function in (3) is referred to as the spatial Green's function. Using the pulse basis and point matching results in the following matrix equation [14][15][16]:…”

“…The FB iterative scheme is applied to the system of equations. The FB method starts with the following decompositions of I and Z as follows [11][12][13][14][15][16]:…”

“…Limit of the Integration k q,max . Equation (16) shows that the integrand decays exponentially with k q . Set the criterion for the convergence of the integral as the integrand decays to a specified value, e 2kq;max Lx 5e 2s ;…”

“…In addition, the FB method has been used in the capacitance extraction for a large array of conducting plate in free space , and the FB method with the SA algorithm (FB/SA) has been employed to accelerate the computational time of large array problems in free space . Furthermore, the generalized FB method is applied for finite planar periodic structures in free space .…”

Homogenization of Periodic Objects Embedded in Layered Media

“…Analytical formulas such as Maxwell-Garnett mixing formula [3] is derived based on spherical inclusions and applied to the case when the size of inclusions is small comparing with the period. In recent years, numerical techniques such as method of moments (MoM), finite difference method (FDM), and finite element method (FEM) have been adopted to solve the problem [4][5][6][7]. The MoM methods usually have better accuracy.…”