Multiple multipole expansions for acoustic scattering

Imhof, Matthias G.

doi:10.1121/1.412122

Cited by 15 publications

(17 citation statements)

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“…Basically, A OJ and A 00 should be scaled by t,. Further details on scaling can be found in the prior paper (Imhof, 1995a).…”

Section: Numerical Results: Acousticsmentioning

confidence: 99%

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Scattering of acoustic and elastic waves using hybrid multiple multipole expansions—Finite element technique

Imhof

1996

The Journal of the Acoustical Society of America

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In this paper, two different methods to solve scattering problems in acoustic or elastic media are coupled to enhance their usefulness. The multiple multipole (MMP) expansions are used to solve for the scattered fields in homogeneous regions which are possibly unbounded. The finite element (FE) method is used to calculate the scattered fields in heterogeneous but bounded scatterers. As the MMP method requires, the different regions and methods are coupled together in the least squares sense. For some examples, the scattered fields are calculated and compared to the analytical solutions. Finally, the seismograms are calculated for a scattering problem with several scatterers, and complex geometries. Thus, the hybrid MMP-FEM technique is a very general and useful tool to solve complex, two-dimensional scattering problems.

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“…Basically, A OJ and A 00 should be scaled by t,. Further details on scaling can be found in the prior paper (Imhof, 1995a).…”

Section: Numerical Results: Acousticsmentioning

confidence: 99%

“…As the name of the method implies, several multipole solutions centered at different positions are often used as expansion functions. The reason to use multiple multipole expansions is their local behavior and thus their ability to model wavefields scattered from complex geometries (Imhof, 1995a). …”

Section: Homogeneous Regions: Multiple Multipole Expansionsmentioning

confidence: 99%

Scattering of acoustic and elastic waves using hybrid multiple multipole expansions—Finite element technique

Imhof

1996

The Journal of the Acoustical Society of America

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“…If the surface is free of tractions, P = 0. Considering time-harmonic waves in the layered medium, the system (Equation (19)) becomes where V and P now denote the Fourier transforms of the corresponding vectors in Equation (19) (functions of ).…”

Section: Antiplane Shearmentioning

confidence: 99%

“…A variety of numerical methods can be applied to Equations (19), (21), (41) and (43). These include conventional finite element and boundary element methods and tailored procedures, such as discontinuous Galerkin methods, that exploit special features of the equations.…”

Section: Plane Strainmentioning

confidence: 99%

“…IKEDA JR AND J. L. TASSOULAS similar to the one described here for the interface locations can be followed for other properties of the layered medium, such as layer moduli. Working with the system of equations (21) and (43), which governs time-harmonic motions (the time-domain counterpart, Equations (19) and (41) can be handled in the same manner), all vectors and matrices are expanded in perturbation series…”

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Wave computations in irregular layered media using a semidiscrete finite element perturbation method

Ikeda

Tassoulas

2008

Numerical Meth Engineering

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SUMMARYA technique that takes into account nonparallel interfaces and lateral inhomogeneities as perturbations with respect to a reference, horizontally layered, laterally homogeneous medium and produces approximations of the perturbed wave motion with little additional computation effort is described. The formulation combines a perturbation method with a semidiscrete finite element technique, providing an approximate treatment of wave propagation in irregular layered media. Consistent transmitting boundaries and other semidiscrete hyperelements as well as Green's functions, already available for regular layered media, can be reformulated within the framework of the method. The method is relevant in problems of foundation dynamics, ground response to seismic waves and site characterization. Example problems are presented toward evaluation of the effectiveness of the method.

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Application of the generalized multipole technique in band structure calculation of two‐dimensional solid/fluid phononic crystals

Shi

Wang

Zhang

2014

Math Methods in App Sciences

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A multiple monopole method based on the generalized multipole technique is presented for the calculation of band structures of two-dimensional mixed solid/fluid phononic crystals. In this method, the fields are expanded by using the fundamental solutions with multiple origins. Besides the sources used to expand the wave fields, an extra monopole source is introduced as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure of the phononic crystals can be obtained. The method can consider the fluid-solid interface conditions and the transverse wave mode in the solid component strictly. Some typical examples are illustrated to discuss the accuracy of the present method. multiply connected domains. The layer potential techniques, which are in the same spirit of the GMT, were developed by Ammari et al. [22][23][24] for studying the wave scattering from high-contrast microstructures, where the spectral properties exhibit a bandgap opening.Recently, the GMT has been developed to calculate the bandgaps of scalar waves in 2D phononic crystals by the present authors [25] based on the method of Reutskiy. Phononic crystals are artificial inhomogeneous composite materials constructed by scatterers periodically embedded in a homogeneous host material and have received a great deal of attention in the last decades [26,27]. The most interesting and important feature of phononic crystals is that such artificial composites can exhibit elastic/acoustic wave bandgaps, in which wave propagation and vibration are all forbidden regardless of the polarization and propagating direction of the elastic/acoustic waves. This behavior leads to many interesting physical properties and potential applications of phononic crystals such as acoustic filters, control of vibration isolation, noise suppression, and design of new transducers [28,29]. In order to determine the band structures and search for the so-called complete phononic bandgaps, an eigenvalue problem has to be solved. For this purpose, several numerical methods have been proposed to compute the band structures. However, some of them have difficulties in dealing with the mixed fluid-solid systems [30,31]. This is due to the fact that different wave modes propagate in solids and fluids, respectively. The mixed longitudinal and transverse elastic waves can propagate in solids, while only the purely longitudinal acoustic wave can propagate in fluids. So the solid-fluid interaction must be taken into account at the interface between the solid and the fluid, which makes it difficult to compute the band structures of phononic crystals composed of solid and fluid components. The widely used plane wave expansion method [26,27] and the recently developed wavelet method [32] were applied to calculate the band structures of mixed solid/fluid phononic crystals by ...

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Multiple multipole expansions for acoustic scattering

Cited by 15 publications

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Scattering of acoustic and elastic waves using hybrid multiple multipole expansions—Finite element technique

Scattering of acoustic and elastic waves using hybrid multiple multipole expansions—Finite element technique

Wave computations in irregular layered media using a semidiscrete finite element perturbation method

Application of the generalized multipole technique in band structure calculation of two‐dimensional solid/fluid phononic crystals

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