On the Numerical Modeling and Solution of a Time Harmonic 3D Wave Equation by Explicit Approximate Inverse Preconditioning

2012 ◽  
Author(s):  
A. Karamouta ◽  
C.K. FilelisPapadopoulos ◽  
G.A. Gravvanis ◽  
M.T. Chryssomallis
Keyword(s):  
Numerical Modeling ◽  
Wave Equation ◽  
Approximate Inverse ◽  
Time Harmonic

On the construction and efficiency of staggered numerical differentiators for the wave equation

Geophysics ◽  
1990 ◽  
Vol 55 (1) ◽  
pp. 107-110 ◽  
Author(s):  
M. Kindelan ◽  
A. Kamel ◽  
P. Sguazzero
Keyword(s):  
Numerical Modeling ◽  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Computational Efficiency ◽  
Differential Operators ◽  
High Order

Finite‐difference (FD) techniques have established themselves as viable tools for the numerical modeling of wave propagation. The accuracy and the computational efficiency of numerical modeling can be enhanced by using high‐order spatial differential operators (Dablain,1986).

Gaussian wave packets in inhomogeneous media with curved interfaces

1987 ◽  
Vol 412 (1842) ◽  
pp. 93-123 ◽  
Keyword(s):  
Wave Equation ◽  
Large Scale ◽  
Evolution Equations ◽  
Wave Packets ◽  
Present Theory ◽  
Orthogonal Direction ◽  
Time Harmonic ◽  
Method Of Solution ◽  
Classical Wave Equation ◽  
The Time Domain

Time-dependent particle-like pulses are considered as asymptotic solutions of the classical wave equation. The wave packets are localized in space with gaussian envelopes. The pulse centres propagate along the rays of the wave equation, and the envelope parameters satisfy evolution equations very similar to the ray equations for time-harmonic disturb­ances. However, the present theory contains an extra degree of freedom not found in the time-harmonic theory. Explicit results are presented for media with constant velocity gradients, and interesting new phenomena are identified. For example, a pulse that is initially long in the direction of propagation and comparatively narrow in the orthogonal direction, maintains its initial spatial orientation even as the propagation direction rotates. The reflection and transmission of a pulse incident upon an interface are also discussed. The various theoretical results are illustrated by numerical simulations. This method of solution could be very useful for fast forward modelling in large-scale structures. It is formulated explicitly in the time domain and does not suffer from unphysical singularities at caustics.

SOLUTION OF TIME-PERIODIC WAVE EQUATION USING MIXED FINITE ELEMENTS AND CONTROLLABILITY TECHNIQUES

2011 ◽  
Vol 19 (04) ◽  
pp. 335-352 ◽  
Author(s):  
SAMI KÄHKÖNEN ◽  
ROLAND GLOWINSKI ◽  
TUOMO ROSSI ◽  
RAINO A. E. MÄKINEN
Keyword(s):  
Periodic Solution ◽  
Wave Equation ◽  
Mixed Finite Elements ◽  
Exact Controllability ◽  
Periodic Wave ◽  
Mixed Formulation ◽  
Absorbing Boundary ◽  
Integrable Functions ◽  
Time Harmonic ◽  
Time Periodic

We consider a controllability method for the time-periodic solution of the two-dimensional scalar wave equation with a first order absorbing boundary condition describing the scattering of a time-harmonic incident wave by a sound-soft obstacle. Solution of the time-harmonic equation is equivalent to finding a periodic solution for the corresponding time-dependent wave equation. We formulate the problem as an exact controllability one and solve the wave equation in time-domain. In a mixed formulation we look for solutions u = (v, p)T. The use of mixed formulation allows us to set the related controllability problem in (L2(Ω))d+1, a space of square-integrable functions in dimension d + 1. No preconditioning is needed when solving this with conjugate gradient method. We present numerical results concerning performance and convergence properties of the method.

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

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