Download or read book High order Two way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering written by Gadi Fibich and published by . This book was released on 2000 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Download or read book Computation of Nonlinear Backscattering Using a High order Numerical Method written by G. Fibich and published by . This book was released on 2001 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

Download or read book Effective Computational Methods for Wave Propagation written by Nikolaos A. Kampanis and published by CRC Press. This book was released on 2008-02-25 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Self focusing Past and Present written by Robert W. Boyd and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-focusing has been an area of active scientific investigation for nearly 50 years. This book presents a comprehensive treatment of this topic and reviews both theoretical and experimental investigations of self-focusing. This book should be of interest to scientists and engineers working with lasers and their applications. From a practical point of view, self-focusing effects impose a limit on the power that can be transmitted through a material medium. Self-focusing also can reduce the threshold for the occurrence of other nonlinear optical processes. Self-focusing often leads to damage in optical materials and is a limiting factor in the design of high-power laser systems. But it can be harnessed for the design of useful devices such as optical power limiters and switches. At a formal level, the equations for self-focusing are equivalent to those describing Bose-Einstein condensates and certain aspects of plasma physics and hydrodynamics. There is thus a unifying theme between nonlinear optics and these other disciplines. One of the goals of this book is to connect the extensive early literature on self-focusing, filament-ation, self-trapping, and collapse with more recent studies aimed at issues such as self-focusing of fs pulses, white light generation, and the generation of filaments in air with lengths of more than 10 km. It also describes some modern advances in self-focusing theory including the influence of beam nonparaxiality on self-focusing collapse. This book consists of 24 chapters. Among them are three reprinted key landmark articles published earlier. It also contains the first publication of the 1964 paper that describes the first laboratory observation of self-focusing phenomena with photographic evidence.

Download or read book The Nonlinear Schr dinger Equation written by Gadi Fibich and published by Springer. This book was released on 2015-03-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France

Download or read book Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves written by Gadi Fibich and published by . This book was released on 2002 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Objects in C written by Yair Shapira and published by CRC Press. This book was released on 2009-06-19 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites, the text covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. Exercises and solutions make the book suitable for classroom use and a supporting website supplies downloadable code.

Download or read book Fundamental Trends in Fluid structure Interaction written by Giovanni P. Galdi and published by World Scientific. This book was released on 2010 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction of a fluid with a solid body is a widespread phenomenon in nature, occurring at different scales and different applied disciplines. Interestingly enough, even though the mathematical theory of the motion of bodies in a liquid is one of the oldest and most classical problems in fluid mechanics, mathematicians have, only very recently, become interested in a systematic study of the basic problems related to fluid-structure interaction, from both analytical and numerical viewpoints. Fundamental Trends in Fluid-Structure Interaction is a unique collection of important papers written by world-renowned experts aimed at furnishing the highest level of development in several significant areas of fluid-structure interactions. The contributions cover several aspects of this discipline, from mathematical analysis, numerical simulation and modeling viewpoints, including motion of rigid and elastic bodies in a viscous liquid, particulate flow and hemodynamic.

Download or read book Numerical Analysis and Its Applications written by Ivan Dimov and published by Springer. This book was released on 2013-10-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.

Download or read book Global discrete artificial boundary conditions for timedependent wave propagation written by and published by DIANE Publishing. This book was released on with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Activities of Institute for Computer Applications in Science and Engineering ICASE written by and published by . This book was released on 2001 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book NASA Langley Scientific and Technical Information Output 2000 written by and published by . This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods for Acoustics Problems written by Frédéric Magoulès and published by . This book was released on 2008 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume presents in eleven chapters key computational methods for acoustics and vibro-acoustics problems. Each chapter, written by different authors, presents a state of the art of well-established or innovative methods, techniques or algorithms. A bibliography is included at the end of each chapter."--BOOK JACKET.

Download or read book Mechanics written by and published by . This book was released on 2001 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Global Discrete Artificial Boundary Conditions for Time dependent Wave Propagation written by Victor S. Ryabenkii and published by DIANE Publishing. This book was released on 2001 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels', nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Download or read book Optimization of Acoustic Source Strength in the Problems of Active Noise Control written by Josip Lončarić and published by . This book was released on 2002 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, that generate the appropriate annihilating acoustic signal (anti-sound). A general solution for the control sources has been obtained previously in both continuous and discrete formulation of the problem. In the current paper, we focus on optimizing the overall absolute acoustic source strength of the control sources. Mathematically, this amounts to the minimization of multi-variable complex-valued functions in the sense of L1 with conical constraints, which are only 'marginally' convex. The corresponding numerical optimization problem appears very challenging even for the most sophisticated state-of-the-art methodologies, and even when the dimension of the grid is small, and the waves are long. Our central result is that the global L1-optimal solution can, in fact, be obtained without solving the numerical optimization problem. This solution is given by a special layer of monopole sources on the perimeter of the protected region. We provide a rigorous proof of the global L1 minimality for both continuous and discrete optimization problems in the one-dimensional case. We also provide numerical evidence that corroborates our result in the two-dimensional case, when the protected domain is a cylinder. Even though we cannot fully justify it, we believe that the same result holds in the general case, i.e., for multi-dimensional settings and domains of arbitrary shape. We formulate it as a conjecture at the end of the paper.

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1804 pages. Available in PDF, EPUB and Kindle. Book excerpt: