A multilevel algorithm for solving a boundary integral equation of wave scattering

Lu, Cai‐Cheng; Chew, Weng Cho

doi:10.1002/mop.4650071013

Cited by 279 publications

(111 citation statements)

References 6 publications

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“…BEMs of complexity lower than that of traditional BEMs, appeared around 1985 with an iterative integral-equation [19,20], in the context of many-particle simulations. The FMM then naturally led to fast multipole boundary element methods (FM-BEMs), whose scope and capabilities have rapidly progressed, especially in connection with application in electromagnetics [21,31,32,53], but also in other fields including acoustics [14,36,48] and computational mechanics [30]. Many of these investigations are summarized in a review article by Nishimura [37].…”

mentioning

confidence: 99%

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

Chaillat

Bonnet

Semblat

2008

Computer Methods in Applied Mechanics and Engineering

103

144

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To reduce computational complexity and memory requirement for 3-D elastodynamics using the boundary element method (BEM), a multi-level fast multipole BEM (FM-BEM) is proposed. The diagonal form for the expansion of the elastodynamic fundamental solution is used, with a truncation parameter adjusted to the subdivision level, a feature necessary for achieving optimal computational efficiency. Both the single-level and multi-level forms of the elastodynamic FM-BEM are considered, with emphasis on the latter. Crucial implementation issues, including the truncation of the multipole expansion, the optimal number of levels, the direct and inverse extrapolation steps are examined in detail with the backing of numerical experiments. A complexity analysis for both the single-level and multi-level versions is conducted. The correctness and computational performances of the proposed elastodynamic FMM are demonstrated on numerical examples, featuring up to O(10 6 ) DOFs run on a single-processor PC and including the diffraction of an incident P plane wave by a semi-spherical or semi-ellipsoidal canyon, representative of topographic site effects.Keywords: Fast multipole method; Boundary element method; 3-D elastodynamics; Topographic site effects IntroductionThe boundary element method (BEM), pioneered in the sixties [6,41], is a mesh reduction method, subject to restrictive constitutive assumptions but yielding highly accurate solutions. It is in particular well suited to deal with unbounded-domain idealizations commonly used in e.g. acoustics [50], electromagnetics [35,39] or seismology [7,22]. In contrast with domain discretization methods, artificial boundary conditions [18] are not needed for dealing with the radiation conditions, and grid dispersion cumulative effects are absent [24,51].However, in traditional boundary element (BE) implementations, the dimensional advantage with respect to domain discretization methods is offset by the fully-populated nature of the BEM coefficient matrix, with set-up and solution times rapidly increasing with the problem size N . It is thus essential to develop alternative, faster strategies that allow to still exploit the known advantages of BEMs when large N prohibit the use of traditional implementations. Fast BEMs, i.e. BEMs of complexity lower than that of traditional BEMs, appeared around 1985 with an iterative integral-equation [19,20], in the context of many-particle simulations. The FMM then naturally led to fast multipole boundary element methods (FM-BEMs), whose scope and capabilities have rapidly progressed, especially in connection with application in electromagnetics [21,31,32,53], but also in other fields including acoustics [14,36,48] and computational mechanics [30]. Many of these investigations are summarized in a review article by Nishimura [37]. The FMM, as well as other fast BEM approaches [23,27,55,56], intrinsically relies upon an iterative solution approach for the linear system of discretized BEM equations, with solution times typically of order O(N lo...

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mentioning

confidence: 99%

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

Chaillat

Bonnet

Semblat

2008

Computer Methods in Applied Mechanics and Engineering

103

144

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Shi¹,

Luan²,

Qin³

et al. 2010

PIER

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Abstract-This paper proposes a multilevel Green's function interpolation method (MLGFIM) to solve electromagnetic scattering from objects comprising both conductor and bi-isotropic objects using volume/surface integral equation (VSIE). Based on equivalence principle, the volume integral equation (VIE) in terms of volume electric and magnetic flux densities and surface integral equation (SIE) in terms of surface electric current density are first formulated for inhomogeneous bi-isotropic and conducting objects, respectively, and then are discretized using the method of moments (MoM). The MLGFIM is adopted to speed up the iterative solution of the resultant equation and reduces the memory requirement. Numerical examples are presented to show good accuracy and versatility of the proposed algorithm in dealing with a wide array of scattering problems.

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“…It inherits the tree structure of the kernel-dependent multilevel fast multipole algorithm (MLFMA) [18][19][20][21][22][23] and combines interpolation ideas of precorrected fast Fourier transform (PFFT) [24][25][26]. The peer-level and lower-toupper level interpolation techniques [14,15] distinguish MLGFIM from Brandt's method in which a soften kernel is required.…”

Section: Introductionmentioning

confidence: 99%

Solution to Electromagnetic Scattering by Bi-Isotropic Media Using Multilevel Green's Function Interpolation Method

Shi

Chan²

2009

PIER

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Abstract-In this paper, a multilevel Green's function interpolation method (MLGFIM) is developed to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional objects comprised of both conductor and bi-isotropic media. The field decomposition method is adopted to split the homogeneous bi-isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi-isotropic material. The problem is formulated using the Paggio-Miller-Chang-Harrington-WuTsai (PMCHWT) approach for multiple homogeneous isotropic media and electric field approach for conducting bodies. The resultant integral equations are discretized by the method of moment (MoM) and iteratively solved by MLGFIM. Numerical examples illustrate accuracy of this algorithm and CPU time of O(N log N ) and memory requirement of O(N ).

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A multilevel algorithm for solving a boundary integral equation of wave scattering

Cited by 279 publications

References 6 publications

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

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

Solution to Electromagnetic Scattering by Bi-Isotropic Media Using Multilevel Green's Function Interpolation Method

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