A new method of computation of wave fields using Gaussian beams

Popov, M. M.

doi:10.1016/0165-2125(82)90016-6

Cited by 328 publications

(195 citation statements)

References 4 publications

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“…Equation (27) for v is then solved, and the total solution u can be obtained by adding the Gaussian beam solution u inc to v in x < 0. It is straight-forward to derive the error equation, i.e.…”

Section: Inflow To the Gridmentioning

confidence: 99%

“…F is time-dependent through its dependence on the Gaussian beam solution, cf. (27). Given the solution at time t, the solution at time t + ∆t can be expressed explicitly using the variation-of-constants formula,…”

Section: Time Integrationmentioning

confidence: 99%

“…For high frequency wave propagation problems the modelling error typically decays in the high frequency limit. This is the case for the method of Gaussian beams [1,5,27,28], which we will consider in this work. A Gaussian beam is a complex-valued basis function with Gaussian profile which is propagated along a classical trajectory.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations

Kieri

Kreiss

Runborg

2015

Adv. Appl. Math. Mech.

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In the semiclassical regime, solutions to the time-dependent Schrödinger equation are highly oscillatory. The number of grid points required for resolving the oscillations may become very large even for simple model problems, making solution on a grid, e.g., using a finite difference method, intractable. Asymptotic methods like Gaussian beams can resolve the oscillations with little effort and yield good approximations when the molecules are heavy and the potential is smooth. However, when the potential has variations on a small length-scale, quantum phenomena become important. Then asymptotic methods are less accurate. The two classes of methods perform well in different parameter regimes. This opens for hybrid methods, using Gaussian beams where we can and finite differences where we have to. We propose a new method for treating the coupling between the finite difference method and Gaussian beams. The new method reduces the needed amount of overlap regions considerably compared to previous methods, which improves the efficiency. We apply the method to scattering problems in one and two dimensions.

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Section: Inflow To the Gridmentioning

confidence: 99%

Section: Time Integrationmentioning

confidence: 99%

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Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations

Kieri

Kreiss

Runborg

2015

Adv. Appl. Math. Mech.

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“…The frequency w is assumed to be large, so that when (2) is substituted into (1), we can treat (1) as a sequence of distinct asymptotic eq~ations. The first such equation comes from the terms that are of order w : (3) This is the eikonal equation of elastodynamics, and can be simplified by writing E -V~, Y = y(l) + y(2), where V(l) and y(2) are the parts of V parallel and perpendicular to E' respectively. Then (3) becomes…”

Section: Mathematical Theorymentioning

confidence: 99%

“…Recent advances [2,3] allow us to incorporate the finite pulse width by means of Gaussian profiles. However, a more realistic model should also include the fact that the pulse is of limited duration and therefore spatially localized in alI directions.…”

mentioning

confidence: 99%

Time Dependent Pulse Propagation and Scattering in Elastic Solids; an Asymptotic Theory

Norris

1987

Review of Progress in Quantitative Nondestructive Evaluation

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Strong scintillation of GNSS signals in the inhomogeneous ionosphere: 1. Theoretical background

Zernov

Gherm

2015

Radio Sci.

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The analytical theory of the Global Navigation Satellite Systems (GNSS) signal propagation through the inhomogeneous ionosphere with time-varying embedded localized random inhomogeneities of electron density is constructed in order to describe the regime of strong scintillation of the wave field propagating in the inhomogeneous ionospheric layer. The theory is based on the solutions of the appropriate Markov's parabolic moment equations, extended to the case of the inhomogeneous background medium. The solutions are validated by the comparison with some rigorous (numerical) solutions known for some limiting cases. The developed theory forms the theoretical background for constructing the physically based software simulator of the random transionospheric GNSS signals.

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A new method of computation of wave fields using Gaussian beams

Cited by 328 publications

References 4 publications

Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations

Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations

Time Dependent Pulse Propagation and Scattering in Elastic Solids; an Asymptotic Theory

Strong scintillation of GNSS signals in the inhomogeneous ionosphere: 1. Theoretical background

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