precorrected-FFT Algorithm Research Articles

Fast Analysis of Broadband Electromagnetic Scattering Characteristics of Electrically Large Targets using Precorrected Fast Fourier Transform Algorithm based on Near Field Matrix Interpolation Method

In this paper, a new method is proposed to analyze the broadband electromagnetic characteristics of electrically large targets by combining the precorrected-FFT algorithm (P-FFT) with the near-field matrix interpolation technique. The proposed method uses the precorrected-FFT algorithm to reduce the storage and accelerate the matrix vector product of the far field. In order to make the precorrected-FFT algorithm can calculate the broadband characteristics of electrically large targets more quickly, the matrix interpolation method is used to interpolate the near-field matrix of the precorrected-FFT algorithm to improve the efficiency of calculation. The numerical results obtained validate the proposed method and its implementation in terms of accuracy and runtime performance.

Sparsity-Aware Precorrected Tensor Train Algorithm for Fast Solution of 2-D Scattering Problems and Current Flow Modeling on Unstructured Meshes

Acceleration of the method of moments (MoM) solution of the volume integral equation (VIE) on unstructured meshes is performed using a precorrected tensor train (P-TT) algorithm. The elements of the MoM’s unstructured mesh are projected onto a regular Cartesian grid. This enables representation of the MoM matrix as the Toeplitz matrix of point-to-point interactions pre- and post-multiplied by sparse matrices projecting MoM’s basis and testing functions on the Cartesian grid. The Toeplitz matrix is subsequently cast into the form of a multidimensional tensor. The latter is decomposed into the product of smaller dimensional matrices also known as tensor train (TT). TT allows to store Toeplitz matrix in $O(\log N)$ memory for VIE with the Laplace kernel and in $O(N \log N)$ memory for VIE with the Helmholtz kernel. Unlike the FFT-based fast algorithms, the P-TT method enables further memory reduction due to the sparsity of sources on the Cartesian grid. This sparsity pattern can be accounted for in construction of TT cores. It further reduces memory use as well as CPU time required for the multiplication of the Toeplitz matrix with a vector. It is shown that upon sufficient sparsity in representation of the sources on the grid, the P-TT algorithm can outperform both in CPU time and memory its FFT-based counterpart known as the precorrected FFT algorithm.

Fast superposition T-matrix solution for clusters with arbitrarily-shaped constituent particles

A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles.

Rapid solution of 3-D oscillatory elastodynamics using the pFFT accelerated BEM

Boundary element method accelerated by the precorrected-FFT algorithm is developed and implemented for 3-D frequency-domain elastodynamic problems. Some critical implementation issues are described. The accuracy and efficiency of the developed method are validated via the comparison between the simulated results and analytical solutions or FEM results of three examples. Excellent agreements are demonstrated in all three examples.

A Three-Dimensional Precorrected FFT Algorithm for Fast Method of Moments Solutions of the Mixed-Potential Integral Equation in Layered Media

A three-dimensional pre-corrected fast Fourier transform (PFFT) algorithm for the rapid solution of the full-dyadic Michalski-Zheng's mixed potential integral equation is presented. The integral equation is discretized with the Rao-Wilton-Glisson (RWG) method of moments. Handling the method of moments interactions with the dyadic kernel is simplified via representation of the RWG functions in terms of barycentric shape functions. The proposed three-dimensional precorrected FFT method distributes two-dimensional FFT grids nonuniformly along the direction of stratification according to conductor locations within the layers. For P two-dimensional FFT grids each with an average of Np associated triangular elements the method exhibits O(P 2 Np logNp) computational complexity and O(P Np) memory usage. The low-frequency breakdown of the integral equation is eliminated via loop-tree decomposition. A unique combination of O(N logN) computational complexity, fully three-dimensional boundary-element modeling in layered substrates, and full-wave modeling from dc to multi-gigahertz frequencies makes the algorithm particularly useful for characterizing large interconnect networks embedded in multilayered substrates. The method is implemented as the electromagnetic solver in Cadence's Virtuoso RF Designer software.

Fast multi‐frequency extraction of 3D impedance based on boundary element method

AbstractFor the boundary element method used in an impedance extractor FastImp, a scheme to handle the boundary integrals is proposed to accelerate the computation for multiple frequencies. Several techniques are combined in the scheme. The near‐field integrals are calculated with a series expansion technique and an approximate formula, whereas the precorrected FFT algorithm is employed for the far‐field integrals. Numerical experiments show that the proposed method is several times faster than FastImp for multi‐frequency extraction, while preserving high accuracy. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2191–2197, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23597

Analysis of scattering by a large array of waveguide-fed wide-slot millimeter wave antennas using precorrected-FFT algorithm

An effective numerical technique employing the precorrected-fast Fourier transform (P-FFT) technique based on the method-of-moments (MoM) is presented to study the scattering from wide-slot antennas fed by waveguides with arbitrary terminations. As the Rao-Wilton-Glisson (RWG) functions are used as the basis and testing functions, the magnetic currents with arbitrary slot directions are considered. In addition, the P-FFT technique is employed to accelerate the MoM procedure for a large slot array. The numerical results are obtained and compared with both the traditional MoM results obtained using the entire-domain basis functions and the experiments results, to demonstrate better effectiveness and accuracy of this technique for millimeter wave scattering from arbitrary wide-slot antennas.

A parallel analysis of the scattering from inhomogeneous dielectric bodies by the volume integral equation and the precorrected‐FFT algorithm

AbstractIn this paper, a parallel implementation of the precorrected fast Fourier transform (FFT) algorithm is presented to efficiently solve the volume‐integral equation for scattering from inhomogeneous dielectric objects. Several examples are given to demonstrate the efficiency and correctness of the message‐passing interface (MPI)‐based parallelization algorithm. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 77–79, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20214

MPI-Based Parallelized Precorrected FFT Algorithm for Analyzing Scattering by Arbitrarily Shaped Three-Dimensional Objects

MPI-Based Parallelized Precorrected FFT Algorithm for Analyzing Scattering by Arbitrarily Shaped Three-Dimensional Objects

MPI-BASED PARALLELIZED PRECORRECTED FFT ALGORITHM FOR ANALYZING SCATTERING BY ARBITRARILY SHAPED THREE-DIMENSIONAL OBJECTS - ABSTRACT

In this paper, how to parallelize the Pre-corrected FFT algorithm for solving the scattering problem of large scale is presented and discussed. The P-FFT technique developed by our group earlier was extended in the current analysis. To show the efficiency of the MPI-based parallelization algorithm, the experiment results are given in the latter part of the paper and various comparisons are made for such a demonstration.

Precorrected-Fft Algorithm for Solving Combined Field Integral Equations in Electromagnetic Scattering

The precorrected-FFT method is applied in this paper to solve the combined field integral equation (CFIE) for scattering by arbitrarily shaped three-dimensional conductors. The object is first discretized using triangular elements with the Rao-Wilton-Glisson (RWG) basis functions. The source singularities on the original triangular meshes are then projected onto uniform rectangular grids, which enables the calculation of the resultant matrix-vector product to be performed by using the fast Fourier transforms. The memory requirement and computational complexity of the resulting algorithm are of O(N1.5) and O(N1.5 log N), respectively, where N denotes the number of unknowns. In addition, the employment of CFIE eliminates the interior resonance problem suffered by both the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) and thus significantly improves the convergence of the iterative solution. A unique advantage of the present method is that the computational expense per iteration of CFIE is almost the same as that of EFIE. This fast algorithm renders problems associated with electromagnetic scattering by large complex objects be handled on a normal personal computer.

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

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 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.