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Journal articles on the topic 'Plane-waves discretization'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Konor, Celal S., and David A. Randall. "Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes." Geoscientific Model Development 11, no. 5 (2018): 1785–97. http://dx.doi.org/10.5194/gmd-11-1785-2018.

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Abstract. We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity

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2

Aminzadeh, F., and J. M. Mendel. "Synthetic vertical seismic profiles for nonnormal incidence plane waves." GEOPHYSICS 50, no. 1 (1985): 127–41. http://dx.doi.org/10.1190/1.1441823.

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Vertical seismic profiles (VSPs) are, by definition, recordings of seismic signals (total upgoing and downgoing seismic wave fields) at different depth points, usually at equally spaced intervals [Formula: see text], i = 1, 2, …, I. In a nonnormal incidence (NNI) elastic model, where each layer is described by thickness, density, and P- and S-wave velocities, the mapping between time and depth needed to generate synthetic VSPs is not usually straightforward. In this paper we develop a relatively simple procedure for generating synthetic vertical and horizontal direction plane wave NNI VSPs. No

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3

Martowicz, Adam, Massimo Ruzzene, Wieslaw J. Staszewski, Julian J. Rimoli, and Tadeusz Uhl. "Out-of-Plane Elastic Waves in 2D Models of Solids: A Case Study for a Nonlocal Discretization Scheme with Reduced Numerical Dispersion." Mathematical Problems in Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/584081.

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The paper addresses the problem of numerical dispersion in simulations of wave propagation in solids. This characteristic of numerical models results from both spatial discretization and temporal discretization applied to carry out transient analyses. A denser mesh of degrees of freedom could be a straightforward solution to mitigate numerical dispersion, since it provides more advantageous relation between the model length scale and considered wavelengths. However, this approach also leads to higher computational effort. An alternative approach is the application of nonlocal discretization sc

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4

Colonius, Tim, Sanjiva K. Lele, and Parviz Moin. "The scattering of sound waves by a vortex: numerical simulations and analytical solutions." Journal of Fluid Mechanics 260 (February 10, 1994): 271–98. http://dx.doi.org/10.1017/s0022112094003514.

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The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered fiel

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5

Cessenat, Olivier, and Bruno Després. "Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation." Journal of Computational Acoustics 11, no. 02 (2003): 227–38. http://dx.doi.org/10.1142/s0218396x03001912.

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This article deals with the use of the Ultra Weak Variational Formulation to solve Helmholtz equation and time harmonic Maxwell equations. The method, issued from domain decomposition techniques, lies in partitioning the domain into subdomains with the use of adapted interface conditions. Going further than in domain decomposition, we make so that the problem degenerates into an interface problem only. The new formulation is equivalent to the weak formulation. The discretization process is a Galerkin one. A possible advantage of the UWVF applied to wave equations is that we use the physical ap

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6

MERCIER, MATTHIEU J., DENIS MARTINAND, MANIKANDAN MATHUR, LOUIS GOSTIAUX, THOMAS PEACOCK, and THIERRY DAUXOIS. "New wave generation." Journal of Fluid Mechanics 657 (July 19, 2010): 308–34. http://dx.doi.org/10.1017/s0022112010002454.

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We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (Exp. Fluids, vol. 42, 2007, pp. 123–130). This mechanism, which involves a tunable source composed of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential is yet to be realized. Our study reveals that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth str

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7

Pai, David M. "Generalized f-k (frequency‐wavenumber) migration in arbitrarily varying media." GEOPHYSICS 53, no. 12 (1988): 1547–55. http://dx.doi.org/10.1190/1.1442436.

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Migration requires one‐way wave continuation. In the spatial domain, one‐way wave equations are derived based on various approximations to an assumed dispersion relation. In the frequency‐wavenumber domain, the well known f-k method and the phase‐shift method are strictly valid only within homogeneous models and layered models, respectively. In this paper, a frequency‐wavenumber domain method is presented for one‐way wave continuation in arbitrarily varying media. In the method, the downward continuation is accomplished, not with plane waves individually as in the f-k or the phase‐shift method

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8

Qi, Hui, Gen Chang Zhang, and Jing Fu Nan. "Ground Motion of Non-Circular Alluvial Valley for Incident Plane SH-Wave." Applied Mechanics and Materials 105-107 (September 2011): 2092–97. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2092.

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The seismic ground motions are studied in an infinite half-space with a non-circular alluvial valley under time harmonic incident anti-plane shear waves. Based on the conformal mapping method and Fourier series expansions, the conditions of displacement continuity and stress equilibrium at the interface of alluvial valley are set as semi-circular alluvial valley in conformal plane, then the result is obtained by constructing a set of infinite linear algebraic equations with boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is

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9

EHRENMARK, ULF T. "On the normal incidence of linear waves over a plane incline partially covered by a rigid lid." Journal of Fluid Mechanics 623 (March 6, 2009): 209–40. http://dx.doi.org/10.1017/s0022112008005296.

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The effect is examined on infinitesimal standing waves over a plane beach when restricted by the arbitrary placing of a finite rigid (or permeable) lid of length ℓ on the undisturbed surface. A uniformly bounded solution for the potential function is obtained by a Green's function method. The Green's function is derived and manipulated, for subsequent computational expedience, from a previously known solution for the problem of an oscillating line source placed at an arbitrary location in the sector. Applications are made to both the case of plate anchored at the origin and the case of plate a

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10

DAVIES, CHRISTOPHER, and PETER W. CARPENTER. "Numerical simulation of the evolution of Tollmien–Schlichting waves over finite compliant panels." Journal of Fluid Mechanics 335 (March 25, 1997): 361–92. http://dx.doi.org/10.1017/s0022112096004636.

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The evolution of two-dimensional Tollmien–Schlichting waves propagating along a wall shear layer as it passes over a compliant panel of finite length is investigated by means of numerical simulation. It is shown that the interaction of such waves with the edges of the panel can lead to complex patterns of behaviour. The behaviour of the Tollmien–Schlichting waves in this situation, particularly the effect on their growth rate, is pertinent to the practical application of compliant walls for the delay of laminar–turbulent transition. If compliant panels could be made sufficiently short whilst r

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11

Kaliberda, M. E., L. M. Lytvynenko, and S. A. Pogarsky. "OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE." Radio physics and radio astronomy 26, no. 3 (2021): 239–49. http://dx.doi.org/10.15407/rpra26.03.239.

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Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper is to develop the operator method to the structures, which scattered fields have both discrete and continuous spatial spectra. Design/methodology/approach: In the spectral domain, in the domain of the Fourier transform, the scattered field is expressed in terms of the unknown Fourier amplitude. The field reflected by the considered structure i

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12

NOLTE, BODO, INGO SCHÄFER, JAN EHRLICH, MARTIN OCHMANN, RALF BURGSCHWEIGER, and STEFFEN MARBURG. "NUMERICAL METHODS FOR WAVE SCATTERING PHENOMENA BY MEANS OF DIFFERENT BOUNDARY INTEGRAL FORMULATIONS." Journal of Computational Acoustics 15, no. 04 (2007): 495–529. http://dx.doi.org/10.1142/s0218396x07003536.

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Different numerical approaches for the physical phenomena of scattering waves from an obstacle are presented. They are based on different integral formulations. Fluid structure interaction effects are numerically treatable as well. We use the Boundary Element Method (BEM) in different approaches because the inherently satisfied Sommerfeld radiation condition makes sure that no reflecting waves from boundaries at infinity occur. One of the biggest disadvantages of numerical methods like BEM is the fact that they have difficulties with handling the high frequency range. For the high frequency ra

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13

Londoño-Arboleda, Mauricio Alejandro, and Hebert Montegranario-Riascos. "Optimal shape parameter for meshless solution of the 2D Helmholtz equation." CT&F - Ciencia, Tecnología y Futuro 9, no. 2 (2019): 15–36. http://dx.doi.org/10.29047/01225383.178.

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The solution of the Helmholtz equation is a fundamental step in frequency domain seismic imaging. This paper deals with a numerical study of solutions for 2D Helmholtz equation using a Gaussian radial basis function-generated finite difference scheme (RBFFD). We analyze the behavior of the local truncation error in approximating partial derivatives of the 2D Helmholtz equation solutions when the shape parameter of RBF varies. For discretization, we performed, by means of a classical numerical dispersion analysis with plane waves, a minimization of the error function to obtain local and adaptiv

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14

GHIDERSA, BRĂDUŢ, and JAN DUšEK. "Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere." Journal of Fluid Mechanics 423 (November 6, 2000): 33–69. http://dx.doi.org/10.1017/s0022112000001701.

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The primary and secondary instabilities of the sphere wake are investigated from the viewpoint of nonlinear dynamical systems theory. For the primary bifurcation, a theory of axisymmetry breaking by a regular bifurcation is given. The azimuthal spectral modes are shown to coincide with nonlinear modes of the instability, which provides a good reason for using the azimuthal expansion as an optimal spectral method. Thorough numerical testing of the implemented spectral–spectral-element discretization allows corroboration of existing data concerning the primary and secondary thresholds and gives

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15

Chatziafratis, A., G. Fikioris, and J. P. Xanthakis. "Exact eigenstates of a nanometric paraboloidal emitter and field emission quantities." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2214 (2018): 20170692. http://dx.doi.org/10.1098/rspa.2017.0692.

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The progress in field emission theory from its initial Fowler–Nordheim form is centred on the transmission coefficient. For the supply (of electrons) function one still uses the constant value due to a supply of plane-waves states. However, for emitting tips of apex radius of 1–5 nm this is highly questionable. To address this issue, we have solved the Schrödinger equation in a sharp paraboloidally shaped quantum box. The Schrödinger equation is separable in the rotationally parabolic coordinate system and we hence obtain the exact eigenstates of the system. Significant differences from the us

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16

Hassan, Hany N. "Numerical Solution of a Boussinesq Type Equation Using Fourier Spectral Methods." Zeitschrift für Naturforschung A 65, no. 4 (2010): 305–14. http://dx.doi.org/10.1515/zna-2010-0407.

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Efficient numerical methods for solving nonlinear wave equations and studying the propagation and stability properties of their solitary waves (solitons) are applied to a Boussinesq type equation in one space dimension. These methods use a pseudospectral (Fourier transform) treatment of the space dependence, together with (a) finite differences, or (b) a fourth-order Runge-Kutta scheme (RK4), for the time evolution. Our schemes follow very accurately single solitons, which are given by simple closed formulas and are known to be stable for all allowed velocities. However, as a parameter of the

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17

Hestholm, Stig. "Elastic tilted orthorhombic (and simpler) wave modeling including free-surface topography." GEOPHYSICS 84, no. 2 (2019): T93—T108. http://dx.doi.org/10.1190/geo2018-0266.1.

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Computational resources have increased in capacity over time — mostly by speed, partly by memory. Consequently, people have continuously explored the possibilities of performing wave modeling and inversion of increasing physical complexity. Achieving a detailed as possible image of the earth’s subsurface improves the success of hydrocarbon exploration, and it is important for other applications, such as archeology, mining, and engineering. I have developed an accurate computational method for elastic wave modeling up to tilted orthorhombic symmetry of anisotropy. The model may be covered by an

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18

ZHENG, TING-HUI, GEORGIOS H. VATISTAS, and ALEX POVITSKY. "SOUND GENERATION BY ONE-CELL AND TWO-CELL VORTICES IN A NONUNIFORM FLOW." Journal of Computational Acoustics 14, no. 03 (2006): 321–37. http://dx.doi.org/10.1142/s0218396x06003074.

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Sound generation by vortical disturbance in a subsonic flow around a cylinder is investigated, using different vortex formulations, by solving both linearized and nonlinear Euler equations numerically. Numerical errors associated with the finite-difference discretization and boundary conditions are kept small using the high-order-accurate spatial differentiation and time marching schemes along with accurate nonreflecting boundary conditions and the sponge layer. If the radial velocity in vortex is assumed equal to zero, the intensity and directivity of acoustic wave patterns appear to be quite

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19

KANG, BONGSU. "DYNAMIC INSTABILITY OF A SPINNING THICK DISK UNDER NONCONSERVATIVE TRACTION." International Journal of Structural Stability and Dynamics 12, no. 05 (2012): 1250040. http://dx.doi.org/10.1142/s021945541250040x.

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This paper presents the dynamic stability analysis of a spinning, thick, annular disk loaded by a circumferentially distributed frictional traction. Considering the automotive/aircraft disc brake as a representative system for this study, the brake rotor is modeled as a spinning annular disk in the context of the Mindlin's thick plate theory to ensure a more accurate estimation of the eigenvalues when the disk involves high circumferential vibration modes that are often observed in unstable disc brake rotors. The frictional traction is decomposed into in-plane and transverse components. The in

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20

Seybert, A. F., and B. Soenarko. "Radiation and Scattering of Acoustic Waves from Bodies of Arbitrary Shape in a Three-Dimensional Half Space." Journal of Vibration and Acoustics 110, no. 1 (1988): 112–17. http://dx.doi.org/10.1115/1.3269465.

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This paper is concerned with the application of the Boundary Integral Equation (BIE) method to acoustic radiation and scattering in a three-dimensional half space. Problems in this class include the radiation of sound from vibrating machines near reflecting surfaces and the scattering of sound from objects in air or water that are in close proximity to rigid or free surfaces. Written in the usual way, the Helmholtz integral formula involves integrations over all surfaces that border the acoustic domain. For half-space problems these integrations include the infinite plane that forms the half-s

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21

Gandzha, Ivan S., and Vasyl P. Lukomsky. "On water waves with a corner at the crest." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2082 (2007): 1597–614. http://dx.doi.org/10.1098/rspa.2007.1840.

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A highly accurate technique for calculating the parameters of the Stokes 120° gravity wave on deep water is proposed. Tanaka's nonlinear transformation of the inverse plane is used to stretch the region near the wave crest for accelerating the convergence of the classical Michell series. Several families of new irregular self-intersecting profiles with a 120° angle at the crest are presented as well. They all degenerate into the Stokes 120° profile as numerical accuracy increases. These solutions seem to represent some kind of the so-called parasitic (or ghost) solutions, which emerge due to d

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22

Farhat, Charbel, Radek Tezaur, and Jari Toivanen. "A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers." International Journal for Numerical Methods in Engineering 78, no. 13 (2009): 1513–31. http://dx.doi.org/10.1002/nme.2534.

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23

Lamhene, Y., M. Tellache, B. Haraoubia, and H. Baudrand. "TRIANGULAR DISCRETISATION FOR ANALYSIS OF MICROSTRIP MITRED BEND, BY AN ITERATIVE METHOD USING THE FAST MODAL TRANSFORM." International Journal of Computing, August 1, 2014, 33–40. http://dx.doi.org/10.47839/ijc.8.2.664.

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In this paper, a study based on iterative method is presented. This method consists in generating a recursive relationship between a wave source and reflected waves from the discontinuity plane which is divided into cells. A high computational speed has been achieved by using Fast Modal Transform (FMT). This work is followed by an application of triangular discretization which offers several advantages over rectangular discretization. The right bend can be simulated by both rectangular and triangular cells, while the mitred bend can be exactly conformed only by the triangular mesh. Deficiencie

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24

Babbush, Ryan, Dominic W. Berry, Jarrod R. McClean, and Hartmut Neven. "Quantum simulation of chemistry with sublinear scaling in basis size." npj Quantum Information 5, no. 1 (2019). http://dx.doi.org/10.1038/s41534-019-0199-y.

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Abstract We present a quantum algorithm for simulating quantum chemistry with gate complexity $$\tilde {\cal{O}}(N^{1/3}\eta ^{8/3})$$ O ̃ ( N 1 ∕ 3 η 8 ∕ 3 ) where η is the number of electrons and N is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity $$\tilde {\cal{O}}(N^{8/3}{\mathrm{/}}\eta ^{2/3})$$ O ̃ ( N 8 ∕ 3 ∕ η 2 ∕ 3 ) . We achieve our scaling in first quantization by performing simulation in the rotating fram

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25

Yang, Lixiang, Yung-Yu Chen, and Sheng-Tao John Yu. "Velocity-Stress Equations for Waves in Solids of Hexagonal Symmetry Solved by the Space-Time CESE Method." Journal of Vibration and Acoustics 133, no. 2 (2011). http://dx.doi.org/10.1115/1.4002170.

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This paper reports an extension of the space-time conservation element and solution element (CESE) method to simulate stress waves in elastic solids of hexagonal symmetry. The governing equations include the equation of motion and the constitutive equation of elasticity. With velocity and stress components as the unknowns, the governing equations are a set of 9, first-order, hyperbolic partial differential equations. To assess numerical accuracy of the results, the characteristic form of the equations is derived. Moreover, without using the assumed plane wave solution, the one-dimensional equa

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26

Dusson, Geneviève. "Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models." IMA Journal of Numerical Analysis, September 19, 2020. http://dx.doi.org/10.1093/imanum/draa052.

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Abstract In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham local density approximation (LDA) models with pseudopotentials, relying on Cancès et al. (2020, Post-processing of the plane-wave approximation of Schrödinger equations. Part I: linear operators. IMA Journal of Numerical Analysis, draa044) for the proofs of such estimates in the case of linear Schrödinger equations. As in Cancès et al. (2016, A perturbation-method-based post-processing for the plane-wave discretization of Kohn–Sham model

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27

Bunting, Gregory, and Scott T. Miller. "Partitioned Coupling for Structural Acoustics." Journal of Vibration and Acoustics 142, no. 1 (2019). http://dx.doi.org/10.1115/1.4045215.

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Abstract We expand the second-order fluid–structure coupling scheme of Farhat et al. (1998, “Load and Motion Transfer Algorithms for 19 Fluid/Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 95–114; 2006, “Provably Second-Order Time-Accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 195(17), pp. 1973–2001) to structural acoustics. The staggered structur

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28

"Discrete mathematical model of the scattering process of E-polarized wave on a periodic impedance grating." V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no. 90 (2019). http://dx.doi.org/10.26565/2221-5646-2019-90-01.

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The method of numerical modeling of wave scattering by periodic impedance grating is considered. In the case of a harmonic dependence of the field on time and the uniformity of the structure along a certain axis, the three-dimensional problem reduces to considering of two 2D problems for the components of the E-polarized and H-polarized waves. The signle nonzero component of the electric field created by the incident E-polarized wave is the solution of the boundary value problem for the Helmholtz equation with Robin boundary conditions. It follows from the physical formulation of the problem t

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29

FAOU, ERWAN, LUDWIG GAUCKLER, and CHRISTIAN LUBICH. "PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION." Forum of Mathematics, Sigma 2 (April 1, 2014). http://dx.doi.org/10.1017/fms.2014.4.

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AbstractPlane wave solutions to the cubic nonlinear Schrödinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are stable over long times that extend to arbitrary negative powers of the smallness parameter. The present paper studies the question as to whether numerical discretizations by the split-step Fourier method inherit such a generic long-time stability property. This can indeed be shown under a condition of linear stability and a nonresonance condition. They

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30

A. Caserta. "A time domain finite-difference technique for oblique incidence of antiplane waves in heterogeneous dissipative media." Annals of Geophysics 41, no. 4 (1998). http://dx.doi.org/10.4401/ag-3800.

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This paper deals with the antiplane wave propagation in a 2D heterogeneous dissipative medium with complex layer interfaces and irregular topography. The initial boundary value problem which represents the viscoelastic dynamics driving 2D antiplane wave propagation is formulated. The discretization scheme is based on the finite-difference technique. Our approach presents some innovative features. First, the introduction of the forcing term into the equation of motion offers the advantage of an easier handling of different inputs such as general functions of spatial coordinates and time. Second

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