Benchmark Calculations for Higher-Order Parabolic Equations PDF Download
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 5
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Book Description
Benchmark solutions generated with parabolic equation (PE) models are presented for range-dependent underwater acoustic propagation problems involving both penetrable and perfectly reflection ocean bottoms. The solution of the wide-angle PE of Claerbout (J.F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976), pp. 206-207) agrees with the outgoing coupled-mode solution for the problems involving penetrable bottoms. The solution of the higher-order PE of Bamberger et al. (Bamberger et al., Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media, SIAM J. Appl. Math. 48, 129-154 (1988)), which is a generalization of Claerbout's PE, agrees with the outgoing coupled-mode solution for problems involving large variations in sound speed and propagation nearly orthogonal to the preferred direction. The computer code FEPE was used to generate the benchmark solutions and was found to run several times faster than the IFDPE computer code due to a tridiagonal system solver in FEPE that is optimized for range-dependent problems.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 5
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Book Description
Benchmark solutions generated with parabolic equation (PE) models are presented for range-dependent underwater acoustic propagation problems involving both penetrable and perfectly reflection ocean bottoms. The solution of the wide-angle PE of Claerbout (J.F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976), pp. 206-207) agrees with the outgoing coupled-mode solution for the problems involving penetrable bottoms. The solution of the higher-order PE of Bamberger et al. (Bamberger et al., Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media, SIAM J. Appl. Math. 48, 129-154 (1988)), which is a generalization of Claerbout's PE, agrees with the outgoing coupled-mode solution for problems involving large variations in sound speed and propagation nearly orthogonal to the preferred direction. The computer code FEPE was used to generate the benchmark solutions and was found to run several times faster than the IFDPE computer code due to a tridiagonal system solver in FEPE that is optimized for range-dependent problems.
Author: Michael D. Collins
Publisher: Springer Nature
ISBN: 1493999346
Category : Science
Languages : en
Pages : 135
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Book Description
This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Author: Nikolaos A. Kampanis
Publisher: CRC Press
ISBN: 1420010875
Category : Mathematics
Languages : en
Pages : 707
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Book Description
Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable
Author: Eric Lex Westreich
Publisher:
ISBN:
Category : Ocean sounds
Languages : en
Pages : 50
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Book Description
Author: Victor A. Galaktionov
Publisher: CRC Press
ISBN: 1482251736
Category : Mathematics
Languages : en
Pages : 565
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Book Description
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
Author: John E Ffowcs Williams
Publisher: World Scientific
ISBN: 9814551724
Category :
Languages : en
Pages : 1028
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Book Description
This conference provided a forum for active researchers to discuss the state of the art in theoretical and computational acoustics. Topics covered structural acoustics, scattering, 3-dimensional propagational problems, fluid/elastic interfaces, wavelets and their impact on acoustics, computational methods and supercomputing.
Author: Pier Paolo Delsanto
Publisher: Taylor & Francis US
ISBN: 9789056995492
Category : Mathematical physics
Languages : en
Pages : 456
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
A higher-order parabolic equation (PE) based on a Pade series and an elastic PE are applied to wave propagation in the ocean. In contrast to the standard PE models of underwater acoustics, the higher-order PE provides accurate solutions for problems involving arbitrarily long ranges, propagation nearly normal to the preferred direction, and large variations in sound speed. The most important applications of the higher-order PE are for problems involving elastic ocean bottoms. A new numerical approach based on centered differences is applied to handle interface conditions. The accuracy of the elastic PE is demonstrated with benchmark calculations. The elastic PE is applied to a range-dependent propagation problem. Reprints. (jhd).
Author: P.C. Etter
Publisher: CRC Press
ISBN: 0203417658
Category : Technology & Engineering
Languages : en
Pages : 447
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Book Description
Underwater Acoustic Modeling and Simulation examines the translation of our physical understanding of sound in the sea into mathematical models that can simulate acoustic propagation, noise and reverberation in the ocean. These models are used in a variety of research and operational applications to predict and diagnose the performance of complex sonar systems operating in the undersea environment. Previous editions of the book have provided invaluable guidance to sonar technologists, acoustical oceanographers and applied mathematicians in the selection and application of underwater acoustic models. Now that simulation is fast becoming an accurate, efficient and economical alternative to field-testing and at-sea training, this new edition will also provide useful guidance to systems engineers and operations analysts interested in simulating sonar performance. Guidelines for selecting and using available propagation, noise and reverberation models are highlighted. Specific examples of each type of model are discussed to illustrate model formulations, assumptions and algorithm efficiency. Instructive case studies demonstrate applications in sonar simulation.
Author: P.C. Etter
Publisher: CRC Press
ISBN: 1482295148
Category : Technology & Engineering
Languages : en
Pages : 447
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Book Description
Underwater Acoustic Modeling and Simulation examines the translation of our physical understanding of sound in the sea into mathematical models that can simulate acoustic propagation, noise and reverberation in the ocean. These models are used in a variety of research and operational applications to predict and diagnose the performance of complex s
