Fast integral equation solvers in computational electromagnetics of complex structures☆

Chew, Weng Cho; Chao, Hsueh-Yung; Cui, Tie Jun; Lu, Cai‐Cheng; Ohnuki, Shinichiro; Pan, Y.C.; Song, Jiming; Velamparambil, S.; Zhao, Junsheng

doi:10.1016/s0955-7997(03)00040-7

Cited by 41 publications

(15 citation statements)

References 104 publications

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“…However, soon the high computational complexity of the IEMs became a major bottleneck in the practical simulations, and so it was crucial to come up with techniques that would reduce the high computational load of the IEMs and enable efficient solutions of large-scale problems. These techniques, known as fast integral equation solvers, significantly extended the usability of the IEMs and made IEMs very compatible with the computationally less expensive PDEMs [6,29].…”

Section: Historical Overviewmentioning

confidence: 99%

“…Traditionally MLFMA has separate algorithms for the static (low frequency) and dynamic (high frequency) cases. The high frequency version is routinely applied for computing scattering by electrically large structures [29], such as an aircraft, but its application to complex antenna geometries, or other structures with a lot of geometrical details that are small compared with the wavelength, is much more challenging. The low frequency version based on for example multipole expansions of the field components [121], on the other hand, becomes inefficient at higher frequencies since the number of terms required in the expansions increases rapidly as the frequency is increased.…”

Section: Broadband Mlfmamentioning

confidence: 99%

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SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

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Abstract-During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.

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Section: Historical Overviewmentioning

confidence: 99%

Section: Broadband Mlfmamentioning

confidence: 99%

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

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“…When r ′ increases, i.e. the points x, y move farther from poles x 0 , y 0 , the exponential in (19) oscillates, reducing the accuracy of G L , see Fig. 5.…”

Section: Empirical Observations In the Real-wavenumber Case (Kmentioning

confidence: 99%

“…The capabilities of the Fast Multipole-Boundary Element Method (FMBEM) and its recursive variant the Multi Level-FMBEM (ML-FMBEM) have rapidly progressed during the last decade, allowing many engineering applications requiring large BEM models, in connection with e.g. acoustics [16], elastodynamics [17], Stokes flows [18] or electromagnetism [19]. Fast BEMs have also been proposed using other approaches, in particular based on hierarchical matrices [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

Grasso

Chaillat

Bonnet

et al. 2012

Engineering Analysis with Boundary Elements

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. Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics. Engineering Analysis with Boundary Elements, Elsevier, 2012Elsevier, , 36, pp.744-758. <10.1016Elsevier, /j.enganabound.2011 Abstract This article extends previous work by the authors on the single-and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region viscoelastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about 3 10 5 boundary unknowns.

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“…4, comprising a source point at and an observer point at that belong to source and observer constellations contained in circles of radius centered about and . It was shown in [33], [43] that the kernel can be expressed as: (13) (14) with , and . Equation (13) realizes a plane wave decomposition of the Hankel function.…”

Section: Plane Wave Decomposition Of the Hankel Kernelmentioning

confidence: 99%

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

Ginste

Michielssen²,

Olyslager

et al. 2006

IEEE Trans. Antennas Propagat.

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Fast integral equation solvers in computational electromagnetics of complex structures☆

Cited by 41 publications

References 104 publications

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

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