A precorrected-FFT method for electrostatic analysis of complicated 3-D structures

Abstract

In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP [1] and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new "precorrected-FFT" algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

Resistances and Inductances Extraction Using Surface Integral Equation With the Acceleration of Multilevel Green Function Interpolation Method

“…There exist several fast algorithms for matrix-vector multiplication that can be used to enhance the efficiency of the solution, such as fast multipole method (FMM) [7][8][9], conjugate gradient fast Fourier transform (CGFFT) [10,11], precorrected FFT (PFFT) [12], the sparse matrix/canonical grid (SMCG) method [13], adaptive integral method (AIM) [14], and MLGFIM [15,16] and so on. Among them, FMM is a fast algorithm with O(N ) complexity, CGFFT, PFFT, SMCG, and AIM are FFT based methods with O(N log N ) complexity, while MLGFIM is based on a hierarchical structure which is similar to FMM but using the Green's function matrix interpolation method with QR [17] factorization technique.…”

Higher Order Hierarchical Legendre Basis Functions Application to the Analysis of Scattering by Uniaxial Anisotropic Objects

“…The basis functions B n take the form of (7). We can obtain the surface currents by solving (8). Then the scattering problem can be solved.…”

“…Several techniques have been proposed to reduce the memory demands as well as the solution complexity of the conventional MoM. Fast integral equation solvers, such as the multilevel fast multiple method (MLFMM) [4,5], adaptive integral method (AIM) [6,7] and its close counterpart, the precorrected FFT (PC-FFT) [8,9], reach the solution complexity and memory requirement as O(N log(N )). However, when the scatter becomes electrically large, the number of unknowns becomes so large that even the fast integral equation solvers cannot solve it efficiently.…”

Multilevel Green's Function Interpolation Method Solution of Volume/Surface Integral Equation for Mixed Conducting/Bi-Isotropic Objects

“…The zeroth order divergence conforming basis functions [28] defined on curvilinear hexahedral and quadrilateral elements are adopted as volume and surface basis functions, respectively. Substituting (2), (5) and (7)- (17) into (18)- (20) and applying Galerkin method, a linear system can be obtained as follows:…”

“…Multilevel fast multipole algorithm (MLFMA) [11][12][13][14], adaptive integral method (AIM) [15][16][17], sparse matrix canonical grid method (SMCG) [18,19] and pre-corrected fast Fourier transform (PFFT) [20,21] etc., have been proposed to fast calculate the field interaction with inhomogeneous isotropic media. More recently, a kernel independent approach, i.e., multilevel Green's function interpolation method (MLGFIM) [22][23][24][25][26][27] has been proposed to solve complex EM problems.…”