- 标题
- 摘要
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- 实验方案
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A Reflectionless Discrete Perfectly Matched Layer
摘要： Perfectly Matched Layer (PML) is a widely adopted non-re?ecting boundary treatment for wave simulations. Reducing numerical re?ections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for the multi-dimensional scalar wave equation which produces no numerical re?ection at all. The re?ectionless discrete PML is discovered through a straightforward derivation using Discrete Complex Analysis. The resulting PML takes an easily-implementable ?nite di?erence form with compact stencil. In practice, the discrete waves are damped exponentially in the PML, and the error due to domain truncation is maintained at machine zero by a moderately thick PML. The numerical stability of the proposed PML is also demonstrated.
关键词： Perfectly matched layers,absorbing boundary,scalar wave equation,discrete complex analysis
更新于2025-09-23 15:23:52
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Spectral analysis for photoacoustic pressure sensor designs: Theoretical model improvement and experimental validation
摘要： In the pulsed laser photoacoustic (PA) detection and spectroscopy applications, the fundamental frequency of the PA signal produced, and the sensor resonance frequency should be as close as possible to each other so that analyzes from the obtained signals can be performed effectively. In order to determine the fundamental frequency of the PA wave, a theoretical model approach based on the development of the frequency domain solution of the PA wave equation is presented for use in the PA pressure sensor designs. For the validation of the theoretical model approach, a PA experimental setup was established, and measurements were made in distilled water. The theoretical and experimental PA frequency spectra were determined to be very compatible with each other. Thus, the theoretical model approach was experimentally validated. According to the theoretical model approach, fundamental frequency values obtained from the experimental measurement results were determined with an average accuracy of ? 4.212%. Furthermore, it has been determined that this value has fallen to ?0.267% in the measurements. With the obtained results from the theoretical model approach, we propose that PA pressure sensors with the more selective and narrower band can be designed for more sensitive detection. Moreover, in this study the effects of different laser parameters such that pulse duration, and laser beam width, on the spectral content of the obtained PA signal are analyzed. These analyses will shed light on the vision of acoustic pressure sensor design by helping to select the most optimum parameters for PA detection.
关键词： Theoretical model approach,Photoacoustic wave equation,Acoustic pressure sensor,Frequency domain solution,Pulsed laser photoacoustic method,Spectroscopy
更新于2025-09-23 15:23:52
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[IEEE 2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL) - Sozopol, Bulgaria (2019.9.6-2019.9.8)] 2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL) - On the Theory of a Pulse Microwave-Pumped Laser
摘要： A new construction of the microwave-pumped laser based on the light-pumping cell that uses radiation of sulfur vapor exposed to electromagnetic waves of the microwave band is described. Advantages of this design are the simple structure, high efficiency of the optical pumping cell, the possibility of cooling the pumping element, and easiness of modifying the emission spectrum of the optical pumping by changing the chemical composition of admixtures in the sulfur light-emitting cell. A mathematical tool for the simulation of the short-pulse operation of the microwave-pumped laser is proposed basing on the generalized wave equation solving for a regular transmission line with essentially nonlinear dispersion characteristic and substantial dissipation. Possible techniques for the numerical solving the generalized wave equation are discussed.
关键词： generalized wave equation,sulfur lamp,numerical simulation,pulse operation,microwave-pumped laser
更新于2025-09-23 15:21:01
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Nonlinear Optics || Wave-Equation Description of Nonlinear Optical Interactions
摘要： We have seen in the last chapter how nonlinearity in the response of a material system to an intense laser field can cause the polarization of the medium to develop new frequency components not present in the incident radiation field. These new frequency components of the nonlinear polarization act as sources of new frequency components of the electromagnetic field. In the present chapter, we examine how Maxwell’s equations describe the generation of these new components, and more generally we see how the various frequency components of the field become coupled by the nonlinear interaction.
关键词： wave equation,electromagnetic field,frequency components,Maxwell’s equations,nonlinear optics,polarization
更新于2025-09-23 15:21:01
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Highly accurate space-time coupled least-squares finite element framework in studying wave propagation
摘要： Simulation of stress wave propagation through solid medium is commonly carried using Galerkin weak-form cast over decoupled space and time domains. In this paper, accuracy of this commonly utilized framework is compared to that of the variationally-consistent least-squares form of the wave equation cast over space-time domain. The two formulations are tested for numerical dispersion and numerical diffusion, through two test cases. The first case studies the dispersion in harmonic shear wave propagation through a soil column over a wide range of forcing frequencies. The second test case investigates numerical diffusion in an axial wave propagation generated by constant force; which is removed after a certain time to allow free vibration to take place. Low numerical dispersion and numerical diffusion as well as high rates of convergence are the main advantages of the coupled least-squares (CLS) computational framework; when compared to the decoupled Galerkin (DG) framework. Based on studies presented here, CLS has low dispersion; yielding errors with one to two orders of magnitude less than that of DG. Also, the numerical diffusion present in DG framework causes a %40 error in DG’s prediction of the stress-wave intensity. Furthermore, accumulative error during evolution is virtually nonexistent for CLS, whereas, the error steadily increases as the solution evolves in DG framework. It is also demonstrated that CLS feature of temporal meshing allows for faster computations.
关键词： Shear wave propagation,Variational-consistency,Higher continuity hierarchical finite elements,Numerical diffusion,Least squares,Impact wave propagation,Space-time coupled,Numerical dispersion,Wave equation
更新于2025-09-23 15:19:57
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X-ray emission from layered media irradiated by an x-ray free-electron laser
摘要： This article presents a computational study of the x-ray ?uorescence induced by the irradiation of thin layered media by intense, short x-ray pulses. The treatment is based on a numerical solution of the Helmholtz wave equation both for the pump and for the ?uorescence signal. Consistently with a possible heating of the medium during the x-ray pulse, complex refractive indices are calculated at each time step from the results of an underlying treatment of atomic physics. In the context of an important core-hole production as a result of photoionization, we discuss the peculiarities of the resulting ampli?ed ?uorescence grazing emission and of the Bragg diffraction which can be realized at some angles inside a multilayer material or even in a perfect crystal.
关键词： multilayer material,x-ray fluorescence,Bragg diffraction,complex refractive indices,photoionization,perfect crystal,Helmholtz wave equation
更新于2025-09-23 15:19:57
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Convergence Analysis of a Discontinuous Galerkin Method for Wave Equations in Second-Order Form
摘要： In this paper we study the convergence property of a spatial discontinuous Galerkin method for wave equations. We prove an optimal convergence rate in the energy norm, which improves an existing suboptimal a priori error estimate. In addition, by adding a penalty term to the variational form, we obtain a supercloseness result, based on which we prove superconvergence of a postprocessed gradient, where the postprocessing operator is the polynomial preserving recovery. All theoretical findings are verified by numerical tests.
关键词： wave equation,supercloseness,discontinuous Galerkin method,superconvergence,PPR
更新于2025-09-19 17:15:36
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On an inverse problem in photoacoustics
摘要： We consider the problem of reconstruction of the Cauchy data for the wave equation in ?3 and ?2 by the measurements of its solution on the boundary of the unit ball.
关键词： wave equation,Inverse problem,photoacoustic
更新于2025-09-19 17:15:36
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AIP Conference Proceedings [AIP Publishing LLC 42ND ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Incorporating the 6th European-American Workshop on Reliability of NDE - Minneapolis, Minnesota (26–31 July 2015)] - An unconditionally-stable numerical method for laser-plasma interactions
摘要： We have previously presented results from a survey of various numerical methods to solve the one-dimensional, cold Maxwell-?uid equations [J. P. Reyes and B. A. Shadwick, AIP Conf. Proc. 1299, 256-261 (2010)]. Using explicit methods, temporal step sizes are constrained by stability conditions and can be much smaller than the time scales involved in the evolution of the ?elds. We introduce an unconditionally-stable Crank-Nicolson method, allowing much larger time steps than is possible with explicit methods. The extra cost in solving implicit equations is negligible compared to the speed up in computational ef?ciency. Using results from a fully-explicit method as a benchmark, we compare results from the implicit method, showing that for the same level of accuracy, the implicit method can take a much larger time step and is far more computationally ef?cient.
关键词： plasma,laser,unconditionally-stable,wave equation
更新于2025-09-12 10:27:22
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Hermite Methods for the Scalar Wave Equation
摘要： Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented. Both methods use (m + 1)d degrees of freedom per node for the displacement in d dimensions; the dissipative and conservative methods achieve orders of accuracy (2m - 1) and 2m, respectively. Stability and error analyses as well as implementation strategies for accelerators are also given.
关键词： Hermite methods,wave equation
更新于2025-09-11 14:15:04