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Автор: Grafiati

Опубліковано: 8 червня 2024

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1

Colton, David, and Rainer Kress. "Time harmonic electromagnetic waves in an inhomogeneous medium." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 116, no. 3-4 (1990): 279–93. http://dx.doi.org/10.1017/s0308210500031516.

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SynopsisWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support, i.e. the permittivity ε = ε(x) and the conductivity σ = σ(x) are functions of x ∊ ℝ3. Existence, uniqueness and regularity results are established for the direct scattering problem. Then, based on existence and uniqueness results for the exterior and interior impedance boundary value problem, a method is presented for solving the inverse scattering problem.

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2

Dassios, G., and K. S. Karadima. "Time harmonic acoustic scattering in anisotropic media." Mathematical Methods in the Applied Sciences 28, no. 12 (2005): 1383–401. http://dx.doi.org/10.1002/mma.609.

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3

Spence, E. A. "Wavenumber-Explicit Bounds in Time-Harmonic Acoustic Scattering." SIAM Journal on Mathematical Analysis 46, no. 4 (January 2014): 2987–3024. http://dx.doi.org/10.1137/130932855.

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4

Kress, Rainer. "Boundary integral equations in time-harmonic acoustic scattering." Mathematical and Computer Modelling 15, no. 3-5 (1991): 229–43. http://dx.doi.org/10.1016/0895-7177(91)90068-i.

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5

Chandler-Wilde, Simon N., and Peter Monk. "Wave-Number-Explicit Bounds in Time-Harmonic Scattering." SIAM Journal on Mathematical Analysis 39, no. 5 (January 2008): 1428–55. http://dx.doi.org/10.1137/060662575.

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6

Ishida, Atsuhide, and Masaki Kawamoto. "Critical scattering in a time-dependent harmonic oscillator." Journal of Mathematical Analysis and Applications 492, no. 2 (December 2020): 124475. http://dx.doi.org/10.1016/j.jmaa.2020.124475.

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7

Shao, Yang, Zhen Peng, Kheng Hwee Lim, and Jin-Fa Lee. "Non-conformal domain decomposition methods for time-harmonic Maxwell equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (April 4, 2012): 2433–60. http://dx.doi.org/10.1098/rspa.2012.0028.

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We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term , are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface integral equation methods. We elucidate a non-conformal integral equation domain decomposition method and a generalized combined field integral equation method for modelling EM wave scattering from non-penetrable and penetrable targets, respectively. Moreover, a plane wave scattering from a composite mockup fighter jet has been simulated using the newly developed multi-solver domain decomposition method.

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8

Hu, Guanghui, Wangtao Lu, and Andreas Rathsfeld. "Time-Harmonic Acoustic Scattering from Locally Perturbed Periodic Curves." SIAM Journal on Applied Mathematics 81, no. 6 (January 2021): 2569–95. http://dx.doi.org/10.1137/19m1301679.

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9

Bao, Gang, Guanghui Hu, and Tao Yin. "Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes." SIAM Journal on Applied Mathematics 78, no. 5 (January 2018): 2672–91. http://dx.doi.org/10.1137/18m1164068.

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10

Zhang, Cheng, Jin Yang, Liu Xi Yang, Jun Chen Ke, Ming Zheng Chen, Wen Kang Cao, Mao Chen, et al. "Convolution operations on time-domain digital coding metasurface for beam manipulations of harmonics." Nanophotonics 9, no. 9 (February 18, 2020): 2771–81. http://dx.doi.org/10.1515/nanoph-2019-0538.

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AbstractTime-domain digital coding metasurfaces have been proposed recently to achieve efficient frequency conversion and harmonic control simultaneously; they show considerable potential for a broad range of electromagnetic applications such as wireless communications. However, achieving flexible and continuous harmonic wavefront control remains an urgent problem. To address this problem, we present Fourier operations on a time-domain digital coding metasurface and propose a principle of nonlinear scattering-pattern shift using a convolution theorem that facilitates the steering of scattering patterns of harmonics to arbitrarily predesigned directions. Introducing a time-delay gradient into a time-domain digital coding metasurface allows us to successfully deviate anomalous single-beam scattering in any direction, and thus, the corresponding formula for the calculation of the scattering angle can be derived. We expect this work to pave the way for controlling energy radiations of harmonics by combining a nonlinear convolution theorem with a time-domain digital coding metasurface, thereby achieving more efficient control of electromagnetic waves.

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11

Colton, David. "Dense sets and far field patterns for acoustic waves in an inhomogeneous medium." Proceedings of the Edinburgh Mathematical Society 31, no. 3 (October 1988): 401–7. http://dx.doi.org/10.1017/s0013091500006799.

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In this paper, we shall obtain two results on the class of far field patterns corresponding to the scattering of time harmonic acoustic plane waves by an inhomogeneous medium of compact support. Although the problem of characterizing the class of far field patterns is of basic importance in inverse scattering theory, very little is known about this class other than the fact that the far field patterns are entire functions of their independent (complex) variables for each positive fixed value of the wave number. In particular, the class of far field patterns is not all of L2(∂Ω) where ∂Ω is the unit sphere and this implies that the inverse scattering problem is improperly posed since the far field patterns are, in practice, determined from inexact measurements. The purpose of this paper is to show that while the class of far field patterns corresponding to the scattering of time harmonic plane waves by an inhomogeneous medium is not all of L2(∂Ω), it is dense in L2(∂Ω) for sufficiently small values of the wave number. In addition, a related result will be obtained for a special translation of the class of far field patterns. Analogous results for the scattering of time harmonic acoustic waves by a homogeneous scattering obstacle have recently been obtained by Colton [1], Colton and Kirsch [2], Colton and Monk [3, 4] and Kirsch [8].

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12

BERMÚDEZ, ALFREDO, LUIS HERVELLA-NIETO, ANDRÉS PRIETO, and RODOLFO RODRÍGUEZ. "VALIDATION OF ACOUSTIC MODELS FOR TIME-HARMONIC DISSIPATIVE SCATTERING PROBLEMS." Journal of Computational Acoustics 15, no. 01 (March 2007): 95–121. http://dx.doi.org/10.1142/s0218396x07003238.

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The aim of this paper is to study the time-harmonic scattering problem in a coupled fluid-porous medium system. We consider two different models for the treatment of porous materials: the Allard–Champoux equations and an approximate model based on a wall impedance condition. Both models are compared by computing analytically their respective solutions for unbounded planar obstacles, considering successively plane and spherical waves. A numerical method combining an optimal bounded PML and finite elements is also introduced to compute the solutions of both problems for more general axisymmetric geometries. This method is used to compare the solutions for a spherical absorber.

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13

Bao, Gang, and Peijun Li. "Inverse medium scattering for three-dimensional time harmonic Maxwell equations." Inverse Problems 20, no. 2 (January 22, 2004): L1—L7. http://dx.doi.org/10.1088/0266-5611/20/2/l01.

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14

Khajah, Tahsin, Xavier Antoine, and Stéphane P. A. Bordas. "B-Spline FEM for Time-Harmonic Acoustic Scattering and Propagation." Journal of Theoretical and Computational Acoustics 27, no. 03 (September 2019): 1850059. http://dx.doi.org/10.1142/s2591728518500597.

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We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing Boundary Conditions (ABCs) are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the numerical method, in particular of the size of the pollution error. Numerical results performed with high-order basis functions (third or fourth order) showed no visible pollution error even for very high frequencies. To prove the ability of the method to increase its accuracy in the high frequency regime, we show how to implement a high-order Padé-type ABC on the fictitious outer boundary. The above-mentioned properties combined with exact geometrical representation make B-Spline FEM a very promising platform to solve high-frequency acoustic problems.

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15

Lu, Wangtao, and Guanghui Hu. "Time-Harmonic Acoustic Scattering from a Nonlocally Perturbed Trapezoidal Surface." SIAM Journal on Scientific Computing 41, no. 3 (January 2019): B522—B544. http://dx.doi.org/10.1137/18m1216195.

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16

Wei, Xing, and Linlin Sun. "Singular boundary method for 3D time-harmonic electromagnetic scattering problems." Applied Mathematical Modelling 76 (December 2019): 617–31. http://dx.doi.org/10.1016/j.apm.2019.06.039.

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17

Vico, Felipe, Miguel Ferrando, Leslie Greengard, and Zydrunas Gimbutas. "The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering." Communications on Pure and Applied Mathematics 69, no. 4 (May 28, 2015): 771–812. http://dx.doi.org/10.1002/cpa.21585.

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18

Hazard, Christophe, and Marc Lenoir. "On the Solution of Time-Harmonic Scattering Problems for Maxwell’s Equations." SIAM Journal on Mathematical Analysis 27, no. 6 (November 1996): 1597–630. http://dx.doi.org/10.1137/s0036141094271259.

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19

Kress, Rainer. "Numerical Solution of Boundary Integral Equations in Time-Harmonic Electromagnetic Scattering." Electromagnetics 10, no. 1-2 (January 1990): 1–20. http://dx.doi.org/10.1080/02726349008908226.

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20

Chen, Zhiming, and Xuezhe Liu. "An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems." SIAM Journal on Numerical Analysis 43, no. 2 (January 2005): 645–71. http://dx.doi.org/10.1137/040610337.

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21

Chen, Zhiming, and Xuezhe Liu. "An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems." SIAM Journal on Numerical Analysis 43, no. 2 (January 2005): 645–71. http://dx.doi.org/10.1137/040610337%\margin.

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22

Luan, Tian, Yao Sun, and Zibo Zhuang. "A meshless numerical method for time harmonic quasi-periodic scattering problem." Engineering Analysis with Boundary Elements 104 (July 2019): 320–31. http://dx.doi.org/10.1016/j.enganabound.2019.03.034.

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23

Bermúdez, A., L. Hervella-Nieto, A. Prieto, and R. Rodríguez. "An Exact Bounded Perfectly Matched Layer for Time-Harmonic Scattering Problems." SIAM Journal on Scientific Computing 30, no. 1 (January 2008): 312–38. http://dx.doi.org/10.1137/060670912.

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24

JOST, GABRIELE. "Integral Equations with Modified Fundamental Solution in Time-Harmonic Electromagnetic Scattering." IMA Journal of Applied Mathematics 40, no. 2 (1988): 129–43. http://dx.doi.org/10.1093/imamat/40.2.129.

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25

Athanasiadis, Christodoulos. "On the acoustic scattering amplitude for a multi-layered Scatterer." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 4 (April 1998): 431–48. http://dx.doi.org/10.1017/s0334270000007736.

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AbstractWe consider the boundary-value problems corresponding to the scattering of a time-harmonic acoustic plane wave by a multi-layered obstacle with a sound-soft, hard or penetrable core. Firstly, we construct in closed forms the normalized scattering amplitudes and prove the classical reciprocity and scattering theorems for these problems. These results are then used to study the spectrum of the scattering amplitude operator. The scattering cross-section is expressed in terms of the forward value of the corresponding normalized scattering amplitude. Finally, we develop a more general theory for scattering relations.

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26

ATASSI, OLIVER V., and AMR A. ALI. "INFLOW/OUTFLOW CONDITIONS FOR TIME-HARMONIC INTERNAL FLOWS." Journal of Computational Acoustics 10, no. 02 (June 2002): 155–82. http://dx.doi.org/10.1142/s0218396x02001668.

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Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vortical disturbances and the scattering of vortical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vortical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.

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27

Dhia, A. S. Bonnet-Ben, J. F. Mercier, F. Millot, S. Pernet, and E. Peynaud. "Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics." Communications in Computational Physics 11, no. 2 (February 2012): 555–72. http://dx.doi.org/10.4208/cicp.221209.030111s.

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AbstractFor the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

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28

Abdelli, S., A. Khalfaoui, T. Kerdja, and D. Ghobrini. "Laser-plasma interaction properties through second harmonic generation." Laser and Particle Beams 10, no. 4 (December 1992): 629–37. http://dx.doi.org/10.1017/s0263034600004559.

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An experimental analysis is conducted to visualize sidescattered second harmonic spectra originating from the critical surface of a plasma produced from a 1, 064-nm laser beam. It is shown that longitudinal and transverse wave-scattering mechanisms producing the second harmonic may also alter the local plasma parameters. These irregular plasma parameter variations and the perturbed spatial uniformity of the incident laser beam can, in turn, be visualized through the second harmonic behavior. This work confirms the origin of the second harmonic production in an inhomogeneous plasma. Time evolution of the optical density of this harmonic showed spectral shifts due to the Doppler effect related to the critical surface dynamics. On the time-integrated spectra, shifted secondary peaks have been observed, indicating that the second harmonic takes its origin also from parametric decay as well as electron decay instability. Other properties of the interaction physics are deduced from the present second harmonic study.

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29

ATHANASIADIS, CHRISTODOULOS. "Scattering theorems for time-harmonic electromagnetic waves in a piecewise homogeneous medium." Mathematical Proceedings of the Cambridge Philosophical Society 123, no. 1 (January 1998): 179–90. http://dx.doi.org/10.1017/s0305004197001977.

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30

Li, Junpu, Lan Zhang, and Qing-Hua Qin. "A regularized method of moments for three-dimensional time-harmonic electromagnetic scattering." Applied Mathematics Letters 112 (February 2021): 106746. http://dx.doi.org/10.1016/j.aml.2020.106746.

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31

Hettlich, F. "Uniqueness of the Inverse Conductive Scattering Problem for Time-Harmonic Electromagnetic Waves." SIAM Journal on Applied Mathematics 56, no. 2 (April 1996): 588–601. http://dx.doi.org/10.1137/s003613999427382x.

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32

Hohage, Thorsten, Frank Schmidt, and Lin Zschiedrich. "Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory." SIAM Journal on Mathematical Analysis 35, no. 1 (January 2003): 183–210. http://dx.doi.org/10.1137/s0036141002406473.

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33

Hu, G., and A. Rathsfeld. "Scattering of time-harmonic electromagnetic plane waves by perfectly conducting diffraction gratings." IMA Journal of Applied Mathematics 80, no. 2 (January 23, 2014): 508–32. http://dx.doi.org/10.1093/imamat/hxt054.

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34

Kress, Rainer. "On the boundary operator in electromagnetic scattering." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 103, no. 1-2 (1986): 91–98. http://dx.doi.org/10.1017/s0308210500014037.

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SynopsisFor radiating solutions to the time-harmonic Maxwell equations, it is shown that the boundary operator mapping the tangential components of the electric field into the tangential components of the magnetic field is a bounded bijective operator from the space of Holder continuous tangential fields with Hölder continuous surface divergence onto itself.

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35

Ngo, Hoang Minh, Ngoc Diep Lai, and Isabelle Ledoux-Rak. "High second-order nonlinear response of platinum nanoflowers: the role of surface corrugation." Nanoscale 8, no. 6 (2016): 3489–95. http://dx.doi.org/10.1039/c5nr07571h.

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36

SAITO, SHINGO, and TOHRU SUEMOTO. "SPATIAL AND MOMENTUM DIFFUSION OF ENERGETIC HOLES IN InAs BY TWO COLOR PUMP-PROBE METHOD." International Journal of Modern Physics B 15, no. 28n30 (December 10, 2001): 3932–35. http://dx.doi.org/10.1142/s0217979201009037.

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Time-resolved electronic Raman scattering of a direct-gap semiconductor, InAs was measured by pump-probe method. We used fundamental pulses and second harmonic pulses of mode-locked Ti:S laser as excitation sources, and fundamental pulses as the probe beam. The time-resolved Raman intensities corresponding to the transition from heavy hole band to light hole band showed different features depending on the excitation energy. In case of the fundamental beam excitation, Raman intensity decreased monotonously. On the contrary, Raman intensity under the second harmonic excitation showed a maximum at a few picosecond after excitation. From the analysis, the temperature of photo-excited hole changed from 5300K to 1300K in 2psec and from 1300K to RT within 4 psec under the second harmonics excitation. It has been shown that the time-resolved Raman scattering measurement is a useful tool to investigate dynamics of the energetic carriers.

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37

Schneider, Stefan. "Application of Fast Methods for Acoustic Scattering and Radiation Problems." Journal of Computational Acoustics 11, no. 03 (September 2003): 387–401. http://dx.doi.org/10.1142/s0218396x03002012.

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Our work is devoted to the solution of large scale (kl = 10…100π) three dimensional radiation and scattering problems covered by the time harmonic Helmholtz equation. We present an application of the Regular Grid Method and Multilevel Fast Multipole Method to acoustic scattering problems. These methods lead to a memory requirement of [Formula: see text] that enables us to solve scattering or radiation problems with several ten-thousands of unknowns. In a computational examples we show the efficiency of these methods.

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38

Morioka, Hisashi. "Generalized eigenfunctions and scattering matrices for position-dependent quantum walks." Reviews in Mathematical Physics 31, no. 07 (July 29, 2019): 1950019. http://dx.doi.org/10.1142/s0129055x19500193.

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We study the spectral analysis and the scattering theory for time evolution operators of position-dependent quantum walks. Our main purpose of this paper is the construction of generalized eigenfunctions of the time evolution operator. Roughly speaking, the generalized eigenfunctions are not square summable but belong to [Formula: see text]-space on [Formula: see text]. Moreover, we derive a characterization of the set of generalized eigenfunctions in view of the time-harmonic scattering theory. Thus we show that the S-matrix associated with the quantum walk appears in the singularity expansion of generalized eigenfunctions.

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39

Mock, Adam. "Calculating Scattering Spectra using Time-domain Modeling of Time-modulated Systems." Applied Computational Electromagnetics Society 35, no. 11 (February 3, 2021): 1288–89. http://dx.doi.org/10.47037/2020.aces.j.351113.

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Obtaining agreement between theoretical predictions that assume single-frequency excitation and finite-difference time-domain (FDTD) simulations that employ broadband excitation in the presence of time-varying materials is challenging due to frequency mixing. A simple solution is proposed to reduce artifacts in FDTD-calculated spectra from the frequency mixing induced by harmonic refractive index modulation applicable to scenarios in which second order and higher harmonics are negligible. Advantages of the proposed method are its simplicity and applicability to arbitrary problems including resonant structures.

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40

Yang, Zhiguo, Li-Lian Wang, and Yang Gao. "A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems." SIAM Journal on Scientific Computing 43, no. 2 (January 2021): A1027—A1061. http://dx.doi.org/10.1137/19m1294071.

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41

Tang, Guangxin, Laurence J. Jacobs, and Jianmin Qu. "Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity." Journal of the Acoustical Society of America 131, no. 4 (April 2012): 2570–78. http://dx.doi.org/10.1121/1.3692233.

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42

Coyle, Joe, and Peter Monk. "Scattering of Time-Harmonic Electromagnetic Waves by Anisotropic Inhomogeneous Scatterers or Impenetrable Obstacles." SIAM Journal on Numerical Analysis 37, no. 5 (January 2000): 1590–617. http://dx.doi.org/10.1137/s0036142998349515.

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43

Barnett, A. H., and T. Betcke. "An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons." SIAM Journal on Scientific Computing 32, no. 3 (January 2010): 1417–41. http://dx.doi.org/10.1137/090768667.

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44

Misici, Luciano, and Francesco Zirilli. "Three-Dimensional Inverse Obstacle Scattering for Time Harmonic Acoustic Waves: A Numerical Method." SIAM Journal on Scientific Computing 15, no. 5 (September 1994): 1174–89. http://dx.doi.org/10.1137/0915072.

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45

Lechleiter, A., and T. Rienmüller. "Time-harmonic acoustic wave scattering in an ocean with depth-dependent sound speed." Applicable Analysis 95, no. 5 (May 21, 2015): 978–99. http://dx.doi.org/10.1080/00036811.2015.1047831.

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46

COLTON, DAVID, and PETER MONK. "THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN A PENETRABLE MEDIUM." Quarterly Journal of Mechanics and Applied Mathematics 40, no. 2 (1987): 189–212. http://dx.doi.org/10.1093/qjmam/40.2.189.

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47

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