Pseudospectral Time-domain Method Research Articles

A Novel Dispersive Time-Domain Interaction Code for Helix TWT by Collocated Space and Staggered Time Scheme Pseudospectral Analytical Time-Domain Method

Remarkable advantages are achieved by pseudospectral techniques such as pseudospectral analytical time-domain (PSATD) method in numerical simulations. Examples are, but not limited to discretization effects reduction (e.g., numerical dispersion error) and geometrical dispersion consideration. In this paper, a novel well-organized version [a newly presented particle-wave interaction code (PaWaIC)], employing collocated space and staggered time scheme PSATD method is introduced: PaWaIC-PSATD-CSST. Validity of the new code is investigated. It is shown that a more accurate phase velocity is realized by PaWaIC-PSATD-CSST in comparison with PaWaIC-pseudospectral arbitrary order finite-difference time-domain (PaWaIC-PSAOFDTD) code for an identical time step and grid size. The fast single-run capability of this novel code for simulating pulse response of wideband tubes is also presented.

Pseudospectral Time Domain Method Implementation Using Finite Difference Time Stepping

Lagrange interpolation polynomials-based Chebyshev pseudospectral time domain (CPSTD) method is an efficient time domain solver for Maxwell equations. Although it has the lowest interpolation error among pseudospectral time domain methods, time derivatives must be calculated using higher order time derivative schemes, such as the Runge–Kutta method. The higher order time derivative methods slow down the computation speed at each step by several folds. In this letter, we show that central finite differences can be used for implementation of time derivatives in CPSTD method. Results are verified by a resonator problem.

Reverse Time Migration of Elastic Waves Using the Pseudospectral Time-Domain Method

Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparound) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel computation, we design a new PML layout which merges the PML in both ends of an axis together. The efficiency and imaging quality of the proposed RTM is verified by imaging on 2D and 3D models.

The Auxiliary Differential Equations Perfectly Matched Layers Based on the Hybrid SETD and PSTD Algorithms for Acoustic Waves

The perfectly matched layer (PML) absorbing boundary condition has been proven to absorb body waves and surface waves very efficiently at non-grazing incidence. However, the traditional PML would generate large spurious reflections at grazing incidence, for example, when the sources are located near the truncating boundary and the receivers are at a large offset. In this paper, a new PML implementation is presented for the boundary truncation in three-dimensional spectral element time domain (SETD) for solving acoustic wave equations. This method utilizes pseudospectral time-domain (PSTD) method to solve first-order auxiliary differential equations (ADEs), which is more straightforward than that in the classical FEM framework.

Single-particle model of a strongly driven, dense, nanoscale quantum ensemble

We study the effects of interatomic interactions on the quantum dynamics of a dense, nanoscale, atomic ensemble driven by a strong electromagnetic field. We use a self-consistent, mean-field technique based on the pseudo-spectral time-domain method, and a full, three-directional basis to solve the coupled Maxwell-Liouville equations. We find that interatomic interactions generate a decoherence in the state of an ensemble on a much faster timescale than the excited state lifetime of individual atoms. We present a novel single-particle model of the driven, dense ensemble by incorporating interactions into a dephasing rate. This single-particle model reproduces the essential physics of the full simulation, and is an efficient way of rapidly estimating the collective dynamics of a dense ensemble.

A Fourier Collocation Approach for Transit-Time Ultrasonic Flowmeter Under Multi-Phase Flow Conditions

A numerical model for a clamp-on transit-time ultrasonic flowmeter (TTUF) under multi-phase flow conditions is presented. The method solves equations of linear elasticity for isotropic heterogeneous materials with background flow where acoustic media are modeled by setting shear modulus to zero. Spatial derivatives are calculated by a Fourier collocation method allowing the use of the fast Fourier transform (FFT) and time derivatives are approximated by a finite difference (FD) scheme. This approach is sometimes referred to as a pseudospectral time-domain method. Perfectly matched layers (PML) are used to avoid wave-wrapping and staggered grids are implemented to improve stability and efficiency. The method is verified against exact analytical solutions and the effect of the time-staggering and associated lowest number of points per minimum wavelengths value is discussed. The method is then employed to model a complete TTUF measurement setup to simulate the effect of a flow profile on the flowmeter accuracy and a study of an impact of inclusions in flowing media on received signals is carried out.

Numerical modeling of pulse propagation through a double-negative metamaterial with adjacent absorptive and gain Lorentz dispersions: A comparison

The state-of-the-art time-domain numerical techniques, the finite-deference time-domain (FDTD) method and the pseudospectral time-domain (PSTD) method, are applied to simulate the physical propagation process of a pulse through a double-negative metamaterial with adjacent absorptive and gain Lorentz dispersions. The algorithmic feasibility and modeling accuracy of the two numerical methods combined with the common techniques for Lorentz dispersion implementation are demonstrated from the obtained simulation results and compared with the analytical solution. It is shown that the FDTD method with material parameters averaged at the slab’s two interfaces works better than that without averaging and also better than the case of PSTD method with the same time and space discretization parameters. The proposed techniques are useful for the ultra-accurate modeling of pulse interaction with metamaterials.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

Auralization of a car pass-by using impulse responses computed with the pseudospectral time-domain method

Car noise is the main environmental noise source in the urban environment. In this paper, a method for auralization of a car pass-by in a street from using a wave-based acoustic prediction method is explored. For the transfer paths between sound source locations and a listener, binaural impulse responses are computed with the pseudospectral time-domain method for various source locations. A dry synthesized car signal is convolved with the binaural impulse responses of the different locations in the street and cross-fade windows are used in order to make the transition between the source positions smooth and continuous. The auralizations are performed for the simplified scenarios where buildings are absent, and for an environment where a long building block is located behind the car. A subjective evaluation was carried out in order to detect the maximum spacing between the discrete source positions that still can produce a perceived continuous car pass-by auralization.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for arbitrary boundary conditions

The wave-based Fourier Pseudospectral time-domain (Fourier-PSTD) method was shown to be an effective way of modeling outdoor acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. A hybrid modeling approach was recently presented to solve the LEE, coupling Fourier-PSTD with the nodal discontinuous Galerkin (DG) time domain method. The hybrid approach allows the computation of complex geometries by using the benefits of the DG methodology at the boundaries while keeping Fourier-PSTD in the bulk of the domain. This paper presents the implementation of arbitrary boundary conditions in the novel methodology, for instance, frequency dependent boundaries. The paper includes an application case of sound propagation for an urban scenario and the comparison of the numerical results with experimental data.

Benchmark cases for urban sound propagation

Urban sound propagation is influenced by multiple reflections on horizontal and vertical surfaces, either specular or diffusive in nature, diffraction around edges and meteorology, causing refraction and scattering of sound waves. This paper initiates multiple benchmark cases for urban sound propagation, with the purpose of comparing the suitability of computational methodologies. The benchmark cases are two-dimensional cross-sections of typical urban geometries, involving all of the effects mentioned above. The sound source is either geometrically screened or is in the line of sight from the receiver's position. When meteorological conditions are included, results obtained from computational fluid dynamics simulations are used. All details of the benchmark cases are concisely described, and results from two numerical methods for outdoor sound propagation are included. Both methods solve the linearized Euler equations (LEE). The first method is the Fourier pseudospectral time-domain method (Fourier-PSTD) implemented in the open source software openPSTD v2.0. The second method is the finite difference time domain method FDTD. A detailed comparison of the results obtained from the two methods is presented.

Reverse Time Migration of Elastic Waves Using the Pseudospectral Time-Domain Method

Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparround) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel ...

The Auxiliary Differential Equations Perfectly Matched Layers Based on the Hybrid SETD and PSTD Algorithms for Acoustic Waves

The perfectly matched layer (PML) absorbing boundary condition has been proven to absorb body waves and surface waves very efficiently at non-grazing incidence. However, the traditional PML would generate large spurious reflections at grazing incidence, for example, when the sources are located near the truncating boundary and the receivers are at a large offset. In this paper, a new PML implementation is presented for the boundary truncation in three-dimensional spectral element time domain (SETD) for solving acoustic wave equations. This method utilizes pseudospectral time-domain (PSTD) method to solve first-order auxiliary differential equations (ADEs), which is more straightforward than that in the classical FEM framework.

Three-dimensional full wave model of image formation in optical coherence tomography.

We demonstrate, what we believe to be, the first mathematical model of image formation in optical coherence tomography, based on Maxwell's equations, applicable to general three-dimensional samples. It is highly realistic and represents a significant advance on a previously developed model, which was applicable to two-dimensional samples only. The model employs an electromagnetic description of light, made possible by using the pseudospectral time-domain method for calculating the light scattered by the sample which is represented by a general refractive index distribution. We derive the key theoretical and computational advances required to develop this model. Two examples are given of image formation for which analytic comparisons may be calculated: point scatterers and finite sized spheres. We also provide a more realistic example of C-scan formation when imaging turbid media. We anticipate that this model will be important for various applications in OCT, such as image interpretation and the development of quantitative techniques.

수중 환경 소음 모델이 적용된 의사 스펙트럼 시간영역 법 합성환경 수중음향채널 모델링 및 시뮬레이션

수중 환경 소음 모델이 적용된 의사 스펙트럼 시간영역 법 합성환경 수중음향채널 모델링 및 시뮬레이션

Incorporating directivity in the Fourier pseudospectral time-domain method using spherical harmonics.

The pseudospectral time-domain method (PSTD) provides an efficient way to solve the linear acoustics equations. With regards to acoustic modeling and auralization, source directivity as well as head-related directivity have a clear influence on the perceived sound field and have to be included in computations. In this paper directive sources are implemented in the time-domain method PSTD. First, a given frequency dependent source directivity is decomposed onto spherical harmonic functions. The directive source is then implemented through spatial distributions in PSTD that relate to the spherical harmonic functions, and time-dependent functions are assigned to the spatial distributions in order to obtain the frequency content of the directivity. Since any directivity function can be expressed as a summation of series of spherical harmonics, the approach can be used to model any type of directive source. For the evaluation of the method, a directivity function was designed analytically and then modeled in PSTD. Octave band analysis was performed and results show a good agreement between the analytical and simulated directivity. A distance related error was observed. However, for distances above 17.5 grid cells from the source center the average error was small (<0.9 dB) at all octave-bands.

Long-Time Instability Analysis of Pseudospectral Time-Domain Method

Lagrange polynomials-based Chebyshev pseudospectral time-domain (CPSTD) method uses Lagrange interpolation polynomials as basis functions to expand electromagnetic fields. Using the field values on all of the grids, Lagrange interpolation polynomials assure global calculation of spatial derivatives rather than local calculations. Because of this global approach, the method has spectral accuracy. Moreover, modeling of complex geometries is possible without introducing additional errors since the method is inherently conformal. Generally, the boundary conditions and multidomain patching are applied through characteristic variables (CVs) approach. However, the method suffers from long-time instability because of the boundary condition implementations. In this paper, the reasons for the instability of the method are analyzed and a stable solution for the cavity resonator simulation is proposed and verified.

Light scattering by hexagonal ice crystals with distributed inclusions

Inclusions of air bubbles or soot particles have significant effects on the single-scattering properties of ice crystals, effects that in turn have significant impacts on the radiation budget of an atmosphere containing the crystals. This study investigates some of the single-scattering effects in the case of hexagonal ice crystals, including effects on the backscattering depolarization ratio, a quantity of practical importance in the interpretation of lidar observations. One distinguishing feature of the study is an investigation of scattering properties at a visible wavelength for a crystal with size parameter (x) above 100, a size regime where one expects some agreement between exact methods and geometrical optics methods. This expectation is generally borne out in a test comparison of how the sensitivity of scattering properties to the distribution of a given volume fraction of included air is represented using (i) an approximate Monte Carlo Ray Tracing (MCRT) method and (ii) a numerically exact pseudo-spectral time-domain (PSTD) method. Another distinguishing feature of the study is a close examination, using the numerically exact Invariant-Imbedding T-Matrix (II-TM) method, of how some optical properties of importance to satellite remote sensing vary as the volume fraction of inclusions and size of crystal are varied. Although such an investigation of properties in the x>100 regime faces serious computational burdens that force a large number of idealizations and simplifications in the study, the results nevertheless provide an intriguing glimpse of what is evidently a quite complex sensitivity of optical scattering properties to inclusions of air or soot as volume fraction and size parameter are varied.

РЕЗОНАНСНЫЕ СВОЙСТВА ДИЭЛЕКТРИЧЕСКОГО МЕТАСЛОЯ

PACS numbers: 81.05.Xj, 78.67.Pt Subject and purpose: The resonant properties are studied of the dielectric metalayer in a form of a doubly periodic structure consisting of silicon parallelepipeds placed on a flat quartz substrate. Design/methodology/approach: Using the pseudospectral timedomain method, numerical simulations of electromagnetic plane wave scattering on the metalayer are made. Resonant properties of the metalayer were experimentally investigated by measuring frequency characteristics of a transmitted electromagnetic wave in a quasi-optical measuring waveguide within 52 to73 GHz. For experimental study, a sample of metalayer was made with the method of mechanical cutting of a layered silicon-quartz structure by a diamond disk. A peculiarity of the studied structure is a double-layer character of the array elements. Each element has a form of a parallelepiped and includes an upper silicon part and a bottom quartz part. A height of the upper part of parallelepiped was changed during the experimental study (the patterned silicon side of the metalayer was polished). Findings: A new technological design of metalayers providing an excitation of high-Q resonances is proposed. The resonances were found to be associated with forming of longitudinal electric or magnetic dipoles in elements of the array and in the substrate. The properties of these kinds of resonances depend on the height of the elements in different ways that allows to control the resonant properties of the structure by selecting the height of the silicon parts. Experimental studies have confirmed the properties of the magnetic dipole resonances predicted theoretically. Conclusions: Performed theoretical and experimental research efforts have demonstrated the opportunity to design all-dielectric resonant metalayers for terahertz applications. Key words: dielectric metalayer, periodic structure, silicon, quartz, transmission resonance, absorption resonance Manuscript submitted 22.12.2015 Radio phys. radio astron. 2016, 21(1): 65-76 REFERENCES 1. AYDIN, K., BULU, I., GUVEN, K., KAFESAKI, M., SOUKOULIS, C. M. and OZBAY, E., 2005. Investigation of magnetic resonances for different split-ring resonator parameters and designs. New J. Phys . vol. 7, id. 168. DOI: 10.1088/1367-630/7/1/168 2. FALCONE, F., LOPETEGI, T., LASO, M. A. G., BAENA, J. D., BONACHE, J., BERUETE, M., MARQUÉS, R., MARTÍN, F. and SOROLLA, M., 2004. Babinet principle applied to the design of metasurfaces and metamaterials. Phys. Rev. Lett . vol. 93, no. 19, id. 197401. DOI: https://doi.org/10.1103/PhysRevLett.93.197401 3. KHARDIKOV, V.V., IARKO, E. O. and PROSVIRNIN, S. L., 2012. Agiant red shift and enhancement of the light confinement in a planar array of dielectric bars. J. Opt . vol. 14, no. 3, id. 035103. DOI: https://doi.org/10.1088/2040-8978/14/3/035103 4. KHARDIKOV, V. V., IARKO, E. O. and PROSVIRNIN, S. L., 2008, Using of transmission matrixes and pseudospectral method in time domain to investigate light diffraction on planar periodic structures. Radio Phys. Radio Astron . vol. 13, no. 2, pp. 146–158 (in Russian). 5. ZHAO, Q., ZHOU, J., ZHANG, F. and LIPPENS, D., 2009. Mie resonance-based dielectric metamaterials. Materials Today . vol. 12, is. 12, pp. 60–69. DOI: https://doi.org/10.1016/S1369-7021(09)70318-9 6. VAN DE GROEP, J. and POLMAN, A., 2013. Designing dielectric resonators on substrates: Combining magnetic and electric resonances. Opt. Express. vol. 21, is. 22, pp. 26285–26302. DOI: https://doi.org/10.1364/OE.21.026285 7. LAMB, J. W., 1996. Miscellaneous data on materials for millimeter and submillimetre optics. Int. J. Infrared Millimeter Waves . vol. 17, no. 12, pp. 1997–2034. DOI: https://doi.org/10.1007/BF02069487 8. KULESHOV, Y. M., 1986. Chapter 8. Measurements in sub-mm wavelength band. In: A. Y. USIKOV, ed. Electronics and Radio Physics of Millimeter and Sub-millimeter Waves . Kyiv: Naukova Dumka Publ., pp. 140–157 (in Russian). 9. The A.Y. Usikov Institute of Radio-Physics and Electronics of National Academy of Sciences of Ukraine, 2008. Quasi-optical radio measuring devices on the basis of a circular hollow dielectric beamguide of submillimeters and millimeters waves [online]. Available from: http://www.ire.kharkov.ua/depquasi/HDB.html

OpenPSTD: The open source pseudospectral time-domain method for acoustic propagation

An open source implementation of the Fourier pseudospectral time-domain (PSTD) method for computing the propagation of sound is presented, which is geared towards applications in the built environment. Being a wave-based method, PSTD captures phenomena like diffraction, but maintains efficiency in processing time and memory usage as it allows to spatially sample close to the Nyquist criterion, thus keeping both the required spatial and temporal resolution coarse. In the implementation it has been opted to model the physical geometry as a composition of rectangular two-dimensional subdomains, hence initially restricting the implementation to orthogonal and two-dimensional situations. The strategy of using subdomains divides the problem domain into local subsets, which enables the simulation software to be built according to Object-Oriented Programming best practices and allows room for further computational parallelization. The software is built using the open source components, Blender, Numpy and Python, and has been published under an open source license itself as well. For accelerating the software, an option has been included to accelerate the calculations by a partial implementation of the code on the Graphical Processing Unit (GPU), which increases the throughput by up to fifteen times. The details of the implementation are reported, as well as the accuracy of the code. Program summaryProgram title: openPSTD v1.1 (v1.0 is the version without the GPU acceleration)Catalogue identifier: AFAA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 45339No. of bytes in distributed program, including test data, etc.: 4139815Distribution format: tar.gzProgramming language: Python (as comes with Blender 2.72).Computer: Variable.Operating system: Windows, Linux, Mac OS X.RAM: From 250 MB for a typical geometry up to 1 GB for large geometries (with about 4M grid points)Classification: 4.3, 12.External routines: Blender 2.72, NumPy, SciPy, PyFFT, PyOpenCL, PyCUDANature of problem: Sound propagationSolution method: Fourier pseudospectral time-domain methodRestrictions: Structured grid, two dimensions, real-valued boundary conditions onlyUnusual features: Implementation of code using Blender/Python including GPU acceleration; subdomain modelling within Fourier pseudospectral methodRunning time: Depending on the dimension of the problem, calculation times take minutes up to hours