scholarly journals Solutions of the Time-Harmonic Wave Equation in Periodic Waveguides: Asymptotic Behaviour and Radiation Condition

2015 ◽  
Vol 219 (1) ◽  
pp. 349-386 ◽  
Author(s):  
Sonia Fliss ◽  
Patrick Joly
Keyword(s):  
Wave Equation ◽  
Asymptotic Behaviour ◽  
Harmonic Wave ◽  
Radiation Condition ◽  
Time Harmonic

A note on diffraction by a right-angled wedge

1965 ◽  
Vol 61 (1) ◽  
pp. 275-278 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Surface Wave ◽  
Harmonic Wave ◽  
Boundary Value ◽  
Normal Derivative ◽  
Support Surface ◽  
Closed Form Solutions ◽  
Time Harmonic

It has been shown in recent years ((5)–(8), (10)) that it is possible to obtain closed form solutions for the time harmonic wave equation when a linear combination of the wave function and its normal derivative is prescribed on the surface of a wedge. Boundary-value problems of this type occur in the problem of diffraction by a highly conducting wedge or by a wedge whose surfaces are thinly coated with dielectric. In certain circumstances such surfaces can support surface waves and one important aspect of the solution of the boundary-value problem is the determination of the amplitude of the surface wave excited.

scholarly journals A new iterative solver for the time-harmonic wave equation

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E57-E63 ◽  
Author(s):  
C. D. Riyanti ◽  
Y. A. Erlangga ◽  
R.-E. Plessix ◽  
W. A. Mulder ◽  
C. Vuik ◽  
...  
Keyword(s):  
Wave Equation ◽  
Linear System ◽  
Time Domain ◽  
Multigrid Method ◽  
Harmonic Wave ◽  
Computational Time ◽  
Full Time ◽  
Iterative Solver ◽  
Time Harmonic ◽  
The Time Domain

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In three dimensions, direct methods cannot be used for problems of practical sizes because the computational time and the amount of memory required become too large. Iterative methods are an alternative. These methods are often based on a conjugate gradient iterative scheme with a preconditioner that accelerates its convergence. The iterative solution of the time-harmonic wave equation has long been a notoriously difficult problem in numerical analysis. Recently, a new preconditioner based on a strongly damped wave equation has heralded a breakthrough. The solution of the linear system associated with the preconditioner is approximated by another iterative method, the multigrid method. The multigrid method fails for the original wave equation but performs well on the damped version. The performance of the new iterative solver is investigated on a number of 2D test problems. The results suggest that the number of required iterations increases linearly with frequency, even for a strongly heterogeneous model where earlier iterative schemes fail to converge. Complexity analysis shows that the new iterative solver is still slower than a time-domain solver to generate a full time series. We compare the time-domain numeric results obtained using the new iterative solver with those using the direct solver and conclude that they agree very well quantitatively. The new iterative solver can be applied straightforwardly to 3D problems.

Uniqueness and non-uniqueness in acoustic tomography of moving fluid

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexey D. Agaltsov ◽  
Roman G. Novikov
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Harmonic Wave ◽  
Acoustic Tomography ◽  
Time Harmonic ◽  
Moving Fluid

AbstractWe consider a model time-harmonic wave equation of acoustic tomography of moving fluid in an open bounded domain in ℝ

scholarly journals Finding scattering data for a time-harmonic wave equation with first order perturbation from the Dirichlet-to-Neumann map

2015 ◽  
Vol 23 (6) ◽  
Author(s):  
Alexey D. Agaltsov
Keyword(s):  
Wave Equation ◽  
Harmonic Wave ◽  
Order Perturbation ◽  
Scattering Data ◽  
Scalar Case ◽  
First Order ◽  
Time Harmonic ◽  
General Scalar ◽  
Dirichlet To Neumann Map ◽  
First Order Perturbation

AbstractWe present formulas and equations for finding scattering data from the Dirichlet-to-Neumann map for a time-harmonic wave equation with first order perturbation with compactly supported coefficients. We assume that the coefficients are matrix-valued in general. To our knowledge, these results are new even for the general scalar case.

Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer

2015 ◽  
Vol 27 (2) ◽  
pp. 264-310 ◽  
Author(s):  
K. E. BOUTARENE ◽  
P.-H. COCQUET
Keyword(s):  
Asymptotic Expansion ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Asymptotic Behaviour ◽  
Harmonic Wave ◽  
Transmission Conditions ◽  
Multi Scale ◽  
Time Harmonic ◽  
Scale Expansion

This work looks at the asymptotic behaviour of the solution to the Helmholtz equation in a penetrable domain of$\mathbb{R}$3with a thin layer of thickness δ which tends to 0. We use the method of multi-scale expansion to derive and justify an asymptotic expansion of the solution with respect to the thickness δ up to any order. We then provide approximate transmission conditions of order two defined on an interface located inside the thin layer, with accuracy up toO(δ2), which allow one to take into account the influence of the thin layer.

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