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The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner. Bayliss, A. and Goldstein, C. I. and Turkel, E. Unspecified Center NASA-CR-172454, NAS 1.26:172454, ICASE-84-49 NAS1-17130; DE-AC02-76CH-00016; RTOP 505-31-83
This book introduces a comprehensive mathematical formulation of the three-dimensional ocean acoustic propagation problem by means of functional and operator splitting techniques in conjunction with rational function approximations. It presents various numerical solutions of the model equation such as finite difference, alternating direction and preconditioning. The detailed analysis of the concept of 3D, N x 2D and 2D problems is very useful not only mathematically and physically, but also computationally. The inclusion of a complete detailed listing of proven computer codes which have been in use by a number of universities and research organizations worldwide makes this book a valuable reference source. Advanced knowledge of numerical methods, applied mathematics and ocean acoustics is not required to understand this book. It is oriented toward graduate students and research scientists to use for research and application purposes.
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
Applied Underwater Acoustics meets the needs of scientists and engineers working in underwater acoustics and graduate students solving problems in, and preparing theses on, topics in underwater acoustics. The book is structured to provide the basis for rapidly assimilating the essential underwater acoustic knowledge base for practical application to daily research and analysis. Each chapter of the book is self-supporting and focuses on a single topic and its relation to underwater acoustics. The chapters start with a brief description of the topic's physical background, necessary definitions, and a short description of the applications, along with a roadmap to the chapter. The subtopics covered within individual subchapters include most frequently used equations that describe the topic. Equations are not derived, rather, assumptions behind equations and limitations on the applications of each equation are emphasized. Figures, tables, and illustrations related to the sub-topic are presented in an easy-to-use manner, and examples on the use of the equations, including appropriate figures and tables are also included. - Provides a complete and up-to-date treatment of all major subjects of underwater acoustics - Presents chapters written by recognized experts in their individual field - Covers the fundamental knowledge scientists and engineers need to solve problems in underwater acoustics - Illuminates, in shorter sub-chapters, the modern applications of underwater acoustics that are described in worked examples - Demands no prior knowledge of underwater acoustics, and the physical principles and mathematics are designed to be readily understood by scientists, engineers, and graduate students of underwater acoustics - Includes a comprehensive list of literature references for each chapter
This series of volumes constitutes an outstanding collection of contributions by the most active research workers in the area of acoustics and mechanics. It brings the reader up to date on the status of the various aspects of research in this field. The volumes should preserve their value for a long time, as they represent a monument to the achievements of human research capabilities in the underwater-acoustics aspects of the environment.
This volume is dedicated to Dr Ding Lee for his untiring efforts in promoting the advancement of theoretical and computational acoustics.This proceedings volume provides a forum for active researchers to discuss the state-of-the-art developments and results in theoretical and computational acoustics, covering aero-, seismo- and ocean acoustics and related topics. It discusses multidimensional wave propagation modeling, methods of computational acoustics, wave propagation in rocks, fluid-solid interfaces, nonlinear acoustics, neural networks, real applications and experimental results.
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Shear waves and closely related interface waves (Rayleigh, Stoneley and Scholte) play an important role in many areas of engineering, geophysics and underwater acoustics. In some cases interest is focused on large-amplitude waves of low frequency such as those associ ated with earthquakes and nuclear explosions; in other cases low amplitude waves, which have often travelled great distances through the sediment, are of interest. Both low and high frequency shear and interface waves are often used for seafloor probing and sediment characterization. As a result of the wide spectrum of different interests, different disciplines have developed lines of research and a literature particularly suited to their own problems. For example water-column acousticians view the seafloor sediment as the lower boundary of their domain and are interested in shear and interface waves in the near bottom sediments mainly from the standpoint of how they influence absorption and reflection at this boundary. On the other hand, geophysicists seeking deep oil deposits are interested in the maximum penetration into the sediments and the tell-tale characteristics of the seismic waves that have encountered potential oil or gas bearing strata. In another area, geotechnical engineers use shear and interface waves to study soil properties necessary for the design and the siting of seafloor structures.