Fourth order schemes for the heterogeneous acoustics equation

Cohen, Gary B.; Joly, Patrick

doi:10.1016/0045-7825(90)90044-m

Cited by 44 publications

(18 citation statements)

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“…Second-order time derivatives terms can also be written in terms of the second-order space derivatives via the Helmholtz equation [14]. Thus, (2) becomes (3) Implementing (3) in the staggered FDTD grid with central differencing in space and a leap-frog discretization in time, we obtain fully discrete update equations for the 3-D AO-FDTD.…”

Section: Update Equations and Stability Analysismentioning

confidence: 99%

“…In order to achieve that, we note that monomials in (15) can be thought of as a basis of an infinite dimensional linear space and (15) as an expansion of in . Therefore, we might as well choose another basis to expand (14), e.g., or , where corresponds to a center frequency, corresponds to the frequency range of interest, and is the th-order first-kind Chebyshev polynomial. In this manner, we are able to better control the frequency response of the dispersion error .…”

Section: Update Equations and Stability Analysismentioning

confidence: 99%

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A three-dimensional angle-optimized finite-difference time-domain algorithm

Wang

Teixeira

2003

IEEE Trans. Microwave Theory Techn.

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Abstract-We present a three-dimensional finite-difference time-domain (FDTD) algorithm to minimize the numerical dispersion error at preassigned angles. Filtering schemes are used to further optimize its frequency response for broad-band simulations. A stability analysis of the resulting FDTD algorithm is also provided. Numerical results show that the dispersion error around any preassigned angle can be reduced significantly in a broad range of frequencies with small computational overhead.

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Section: Update Equations and Stability Analysismentioning

confidence: 99%

Section: Update Equations and Stability Analysismentioning

confidence: 99%

A three-dimensional angle-optimized finite-difference time-domain algorithm

Wang

Teixeira

2003

IEEE Trans. Microwave Theory Techn.

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“…In recent years there has appeared some papers dealing with the construction of high order schemes for wave equation and other hyperbolic equations, see [1,3,4,5,7,8,9,10,11] and references therein .…”

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confidence: 99%

On the construction of arbitrary order schemes for the many dimensional wave equation

Tuomela¹

1996

Bit Numer Math

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“…Alford, Kelly, and Boore [2], Marfurt [29], Dablain [9], and Sei [34] present higher-order algorithms for the elastic wave equation. Similarly, higher-order finitedifference methods have been developed for acoustic applications by Gottlieb and Turkel [13], Cohen and Joly [8], and Davis [10], for example.…”

mentioning

confidence: 99%

“…Related methods for the second-order wave equation are presented by Cohen and Joly [8] and Shubin and Bell [39].…”

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confidence: 99%

Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation

Zingg¹

2000

SIAM J. Sci. Comput.

145

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Abstract. This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fully-discrete finite-difference methods are studied: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. The results provide a clear understanding of the relative merits of the methods compared, especially the trade-offs associated with the use of optimized methods. A numerical example is given which shows that the benefits of an optimized scheme can be small if the waveform has broad spectral content.Key words. finite-difference methods, wave propagation, electromagnetics, acoustics, Maxwell equations AMS subject classifications. 65M05, 78A40, 78M20, 76Q05PII. S1064827599350320Introduction. Numerical simulation can play an important role in the context of engineering design and in improving our understanding of complex systems. The simulation of wave phenomena, including electromagnetic, elastic, and acoustic waves, is an area of active research. Lighthill [24] and Taflove [40] discuss the prospects for computational aeroacoustics and electromagnetics, respectively. The computational requirements for accurate simulations of the propagation and scattering of waves can be high, particularly if the size of the geometry under study is much larger than the wavelength. Consequently, there has been considerable recent effort directed towards improving the efficiency of numerical methods for simulating wave phenomena.In electromagnetics, the most popular approach to the numerical solution of the time-domain Maxwell equations for numerous applications has been the algorithm of Yee [50], which was named the finite-difference time-domain (FDTD) method by Taflove [41]. This algorithm combines second-order centered differences on a staggered grid in space with second-order staggered leapfrog time marching. Its main attributes are its very low cost per grid node and lack of dissipative error. Yee's method is often applied using Cartesian grids, with a special treatment of curved boundaries [20]. Extension to curvilinear grids was carried out by Fusco [11]. Madsen and Ziolowski [28] put the method into a finite-volume framework applicable to unstructured grids. Vinokur and Yarrow [47,48] developed a related finite-surface method with advantages at boundaries and grid singularities.Other methods which have been successfully app...

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Fourth order schemes for the heterogeneous acoustics equation

Cited by 44 publications

References 9 publications

A three-dimensional angle-optimized finite-difference time-domain algorithm

A three-dimensional angle-optimized finite-difference time-domain algorithm

On the construction of arbitrary order schemes for the many dimensional wave equation

Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation

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