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Discrete Ordinates Transport Methods For Problems With Highly Forward Peaked Scattering
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Book Synopsis New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations by : Jacques Tagoudjeu
Download or read book New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and published by Universal-Publishers. This book was released on 2011-04 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.
Book Synopsis The Use of Computers in Radiation Therapy by : Wolfgang Schlegel
Download or read book The Use of Computers in Radiation Therapy written by Wolfgang Schlegel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computers have had and will continue to have a tremendous impact on professional activity in almost all areas. This applies to radiological medicine and in particular to radiation therapy. This book compiles the most recent developments and results of the application of computers and computer science as presented at the XIIIth International Conference on the Use of Computers in Radiation Therapy in Heidelberg, Germany. The text of both oral presentations and posters is included. The book is intended for computer sientists, medical physicists, engineers and physicians in the field of radiation therapy and provides a comprehensive survey of the entire field.
Author :Alexander A. Kokhanovsky Publisher :Springer Science & Business Media ISBN 13 :3540684352 Total Pages :366 pages Book Rating :4.5/5 (46 download)
Book Synopsis Light Scattering Reviews 2 by : Alexander A. Kokhanovsky
Download or read book Light Scattering Reviews 2 written by Alexander A. Kokhanovsky and published by Springer Science & Business Media. This book was released on 2007-04-29 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is to continue the Light Scattering Reviews series devoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. It gives a valuable picture of recent developments in the area of remote sensing and radiative transfer. The work has capabilities to further facilitate studes in light scattering media optics and be of importance for researchers across various scientific fields including astronomy, meterology and geophysics.
Book Synopsis Computational Methods in Transport by : Frank Graziani
Download or read book Computational Methods in Transport written by Frank Graziani and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 1174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1992 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2001 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nuclear Computational Science by : Yousry Azmy
Download or read book Nuclear Computational Science written by Yousry Azmy and published by Springer Science & Business Media. This book was released on 2010-04-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.
Download or read book Reactor Technology written by and published by . This book was released on 1970 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Radiology and Imaging by : Christoph Börgers
Download or read book Computational Radiology and Imaging written by Christoph Börgers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles collected in this volume are based on lectures given at the IMA Workshop, "Computational Radiology and Imaging: Therapy and Diagnostics", March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near-infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning. Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative methods for large linear and non-linear least-squares problems, iterative methods for linear feasibility problems, and optimization methods. The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non-specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.
Book Synopsis Springer Series in Light Scattering by : Alexander Kokhanovsky
Download or read book Springer Series in Light Scattering written by Alexander Kokhanovsky and published by Springer. This book was released on 2019-01-13 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a survey of modern theoretical techniques in studies of radiative transfer and light scattering phenomena in turbid media. It offers a comprehensive analysis of polarized radiative transfer, and also discusses advances in planetary spectroscopy as far as aerosol layer height determination is of interest. Further, it describes approximate methods of the radiative transfer equation solution for a special case of strongly scattering media. A separate chapter focuses on optical properties of Black Carbon aggregates.
Author :Alexander A. Kokhanovsky Publisher :Springer Science & Business Media ISBN 13 :3642103367 Total Pages :549 pages Book Rating :4.6/5 (421 download)
Book Synopsis Light Scattering Reviews 5 by : Alexander A. Kokhanovsky
Download or read book Light Scattering Reviews 5 written by Alexander A. Kokhanovsky and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Light scattering by densely packed inhomogeneous media is a particularly ch- lenging optics problem. In most cases, only approximate methods are used for the calculations. However, in the case where only a small number of macroscopic sc- tering particles are in contact (clusters or aggregates) it is possible to obtain exact results solving Maxwell’s equations. Simulations are possible, however, only for a relativelysmallnumberofparticles,especiallyiftheirsizesarelargerthanthewa- length of incident light. The ?rst review chapter in PartI of this volume, prepared by Yasuhiko Okada, presents modern numerical techniques used for the simulation of optical characteristics of densely packed groups of spherical particles. In this case, Mie theory cannot provide accurate results because particles are located in the near ?eld of each other and strongly interact. As a matter of fact, Maxwell’s equations must be solved not for each particle separately but for the ensemble as a whole in this case. The author describes techniques for the generation of shapes of aggregates. The orientation averaging is performed by a numerical integration with respect to Euler angles. The numerical aspects of various techniques such as the T-matrix method, discrete dipole approximation, the ?nite di?erence time domain method, e?ective medium theory, and generalized multi-particle Mie so- tion are presented. Recent advances in numerical techniques such as the grouping and adding method and also numerical orientation averaging using a Monte Carlo method are discussed in great depth.
Book Synopsis Proceedings of the Topical Meeting on Radiation Protection for Our National Priorities by :
Download or read book Proceedings of the Topical Meeting on Radiation Protection for Our National Priorities written by and published by . This book was released on 2000 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Methods and Experimental Measurements XIII by : C. A. Brebbia
Download or read book Computational Methods and Experimental Measurements XIII written by C. A. Brebbia and published by WIT Press. This book was released on 2007 with total page 929 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing papers presented at the Thirteenth International Conference in this well established series on (CMEM) Computational Methods and Experimental Measurements. These proceedings review state-of-the-art developments on the interaction between numerical methods and experimental measurements.Featured topics include: Computational and Experimental Methods; Experimental and Computaqional Analysis; Computer Interaction and Control of Experiments; Direct, Indirect and In-Situ Measurements; Particle Methods; Structural and Stress Analysis; Structural Dynamics; Dynamics and Vibrations; Electrical and Electromagnetic Applications; Biomedical Applications; Heat Transfer; Thermal Processes; Fluid Flow; Data Acquisition; Remediation and Processing and Industrial Applications.
Book Synopsis SIAM Journal on Scientific Computing by :
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 1996 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Papers on Multiple Scattering in Plane Parallel Atmospheres and Oceans by : George W. Kattawar
Download or read book Selected Papers on Multiple Scattering in Plane Parallel Atmospheres and Oceans written by George W. Kattawar and published by . This book was released on 1991 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods in Multidimensional Radiative Transfer by : Guido Kanschat
Download or read book Numerical Methods in Multidimensional Radiative Transfer written by Guido Kanschat and published by Springer Science & Business Media. This book was released on 2008-12-24 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.
