Fast and efficient algorithms in computational electromagnetics

2006

Radio Science, 2004

Time domain boundary integrals are used to impose global transparent boundary conditions in two-dimensional finite difference time domain solvers. Augmenting classical methods for imposing these conditions with the multilevel plane wave time domain scheme reduces the computational cost of enforcing a global transparent boundary condition from O( Ñs 2 Ñ t 2 ) to O( Ñs Ñ t log Ñ s log Ñ t ); here Ñs and Ñ t denote the number of equivalent source boundary nodes and their time samples used to integrate external fields, respectively. Numerical results demonstrate that for thin and concave material objects, plane wave time domain-accelerated global transparent boundary kernels outperform perfectly matched layer-based absorbing boundary schemes without loss of accuracy.

IEEE Transactions on Antennas and Propagation, 2004

The adaptive integral method (AIM) is implemented in conjunction with the loop-tree (LT) decomposition of the electric current density in the method of moments approximation of the electric field integral equation. The representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic (EM) simulation without low-frequency numerical instability problems, while scaling of computational complexity and memory storage with the size of the problem of the are of the same order as in the conventional AIM algorithm. The proposed algorithm is built as an extension to the conventional AIM formulation that utilizes roof-top expansion functions, thus providing direct and easy way for the development of the new stable formulation when the roof-top based AIM is available. A new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested. The discussed preconditioner can be used with both roof-top and LT formulations of AIM and other fast algorithms. The resulting AIM implementation is validated through its application to the broadband, EM analysis of large microstrip antennas and planar interconnect structures. Index Terms-Fast algorithms, full-wave electromagnetic (EM) CAD, loop-tree (LT) decomposition, low frequency, method of moments (MoM).

An efficient Multilevel Fast Multipole Algorithm (MLFMA) for the modeling of very large planar microwave circuits is presented. The method relies on an Electric Field Integral Equation (EFIE) formulation and a series expansion of the pertinent Green dyadic, based on the use of Perfectly Matched Layers (PML). The new PML-MLFMA is implemented in order to accelerate the numerous matrix-vector multiplications appearing in the iterative solution of the problem. The computational and memory complexity of the algorithm scale down to O(N ) for electrically large structures. The method is illustrated by means of illustrative, numerical examples.

IEEE Transactions on Antennas and Propagation, 2004

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling^directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling^directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single^is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms. Index Terms-Electromagnetic scattering, fast far-field approximation (FAFFA), method of moments, multilevel fast multipole algorithm, multilevel ray-propagation fast multipole algorithm.

2021

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization, the number of MC samples has to be large. In this paper, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme. Index Terms-Fast Fourier transform (FFT), fast multipole method (FMM), integral equation, multilevel Monte Carlo method (MLMC), numerical methods, uncertain geometry, uncertainty quantification.

IEEE Transactions on Antennas and Propagation, 2000

A fast algorithm is presented for solving electric, magnetic, and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as ( 3 2 log ) as opposed to ( 2 ) for classical MOT methods, where and are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented.

IEEE Journal on Multiscale and Multiphysics Computational Techniques

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme. Index Terms-uncertainty quantification, uncertain geometry, numerical methods, multilevel Monte Carlo method (MLMC), integral equation, fast multipole method (FMM), fast Fourier transform (FFT).

Innovative Architecture for Future Generation High-Performance Processors and Systems (Cat. No.PR00650)

In recent years, the Multilevel Fast Multipole Method (MLFMA) [14, 171 has been developed into one of the most powerjul techniques for accelerating the iterative solution of integral equations of electromagnetics. It has been shown that the MLFMA reduces the computational complexity of a matrix-vector multiply from O ( N 2

IEEE Transactions on Antennas and Propagation, 2000

The fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies. Each can operate in their respective regimes, but are not tenable in the other regimes. The paper reports on a way to factorize the Green's function for fast algorithm using a mixed form. The low-frequency fast multipole algorithm (LF-FMA) will be used at low frequencies or the long-wavelength regime, and the multilevel fast multipole algorithm (MLFMA) will be used for the mid frequencies or the shorter-wavelength regime. For object modeling where both long-wavelength and wave physics are important, we propose a mixed-form fast multipole algorithm (MF-FMA). This algorithm has no low frequency break down, and it can work seamlessly from static (where circuit physics is important) to dynamic (where wave physics is important).