A fast directional algorithm for high-frequency electromagnetic scattering

Tsuji, Paul H.; Ying, Lexing

doi:10.1016/j.jcp.2011.02.013

Cited by 7 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the algorithm can be adapted to handle kernels other than the Helmholtz kernel quite easily, which is not true for most other existing algorithms. The algorithm was used to accelerate the BEM for electromagnetic scattering problems by Tsuji and Ying in [27]. However, to the best of the authors' knowledge, no reported work is devoted to the application of the algorithm to accelerating BEM for the Burton-Miller BIE, which is essential for solving real-world acoustic problems.…”

Section: Introductionmentioning

confidence: 99%

A fast directional BEM for large-scale acoustic problems based on the Burton–Miller formulation

Cao

Wen

Xiao

et al. 2015

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

In this paper, a highly efficient fast boundary element method (BEM) for solving largescale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton-Miller boundary integral equation (BIE), thus the fictitious frequency issue is completely avoided. The BIE is discretized by using the Nyström method based on the curved quadratic elements, leading to simple numerical implementation (no edge or corner problems) and high accuracy in the BEM analysis. The linear systems are solved iteratively and accelerated by using a newly developed kernel-independent wideband fast directional algorithm (FDA) for fast summation of oscillatory kernels. In addition, the computational efficiency of the FDA is further promoted by exploiting the low-rank features of the translation matrices, resulting in two-to three-fold reduction in the computational time of the multipole-tolocal translations. The high accuracy and nearly linear computational complexity of the present method are clearly demonstrated by typical examples. An acoustic scattering problem with dimensionless wave number kD (where k is the wave number and D is the typical length of the obstacle) up to 1000 and the degrees of freedom up to 4 million is successfully solved within 10 hours on a computer with one core and the memory usage is 24 GB.

show abstract

Section: Introductionmentioning

confidence: 99%

A fast directional BEM for large-scale acoustic problems based on the Burton–Miller formulation

Cao

Wen

Xiao

et al. 2015

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

show abstract

“…We have scaled the problem such that the wave length equals one and thus high frequencies correspond to problems with large computational domains, i.e., large K. The computation in Equation 1.1 arises in electromagnetic and acoustic scattering, where the usual partial differential equations are transformed into boundary integral equations (BIEs) [16,24,34,36]. The discretized BIEs often result in large, dense linear systems with N = O(K 2 ) unknowns, for which iterative methods are used.…”

mentioning

confidence: 99%

“…The computation in Equation 1.1 arises in electromagnetic and acoustic scattering, where the usual partial differential equations are transformed into boundary integral equations (BIEs) [16,24,34,36]. The discretized BIEs often result in large, dense linear systems with N = O(K 2 ) unknowns, for which iterative methods are used.…”

mentioning

confidence: 99%

A Parallel Directional Fast Multipole Method

Benson¹,

Poulson²,

Tran³

et al. 2014

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

Abstract. This paper introduces a parallel directional fast multipole method (FMM) for solving N -body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We propose a simple partition at a fixed level of the octree and show that, if the partitions are properly balanced between p processes, the overall runtime is essentially O(N log N/p+ p). By the structure of the low-rank criterion, we are able to avoid communication at the top of the octree. We demonstrate the effectiveness of our parallelization on several challenging models.

show abstract

“…One general category of the application is the Fourier-based physics equation solver and analysis [2], [3], [26], [27], [7]. For example, when solving the volume integral equations in electromagnetics through the well-known conjugate-gradient fast Fourier transform method, the computation of the Fourier transform for the electric current density are needed.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Fourier transform (FT), as a most important tool for spectral analyses, is often encountered in computational physics, including areas such as electromagnetics [1], [2], [3], [4], image processing [5], [6] and acoustics [7], [8].…”

Section: Introductionmentioning

confidence: 99%

An Accurate Conformal Fourier Transform Method for 3D Discontinuous Functions

Zhu

Liu

2015

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

Fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas. In this work, a highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to evaluate the finite Fourier transform of 3D discontinuous functions. A curved tetrahedron mesh combined with curvilinear coordinate transform, instead of the Cartesian grid, is adopted to flexibly model an arbitrary shape of the discontinuity boundary. This enables us to take full advantages of high order interpolation and Gaussian quadrature methods to achieve highly accurate Fourier integration results with a low sampling density. The 3D nonuniform fast Fourier transform (NUFFT) helps to keep the complexity of the proposed algorithm to that similar to the traditional 3D FFT algorithm. Therefore, the proposed CFT algorithm can achieve order of magnitude higher accuracy than 3D FFT with lower sampling density and similar computation time. The convergence is proved and verified.

show abstract

A fast directional algorithm for high-frequency electromagnetic scattering

Cited by 7 publications

References 30 publications

A fast directional BEM for large-scale acoustic problems based on the Burton–Miller formulation

A fast directional BEM for large-scale acoustic problems based on the Burton–Miller formulation

A Parallel Directional Fast Multipole Method

An Accurate Conformal Fourier Transform Method for 3D Discontinuous Functions

Contact Info

Product

Resources

About