Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions
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Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions
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Author : W. Freeden
language : en
Publisher:
Release Date : 1985
Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions written by W. Freeden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Geodesy categories.
Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions
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Author : Willi Freeden
language : en
Publisher:
Release Date : 1985
Computation Of Spherical Harmonics And Approximation By Spherical Harmonic Expansions written by Willi Freeden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Gravity categories.
A technique is developed for generating spherical harmonics by exact computation (in integer mode) thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials. Exact computation of (maximal) linearly independent and orthonormal systems of spherical harmonics is explained using exclusively integer operations. The numerical efficiency is discussed. The development of exterior gravitational potential in a series of outer (spherical) harmonics is investigated. Some numerical examples are given for solving exterior Dirichlet's boundary-value problems by use of outer (spherical) harmonic expansions for not-necessarily spherical boundaries. Keywords: Homogeneous harmonic polynomials; Spherical harmonics; Exact computation in integer mode; Series expansion into spherical harmonics; Exterior dirichlet's problem.
Spherical Harmonics And Approximations On The Unit Sphere An Introduction
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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-17
Spherical Harmonics And Approximations On The Unit Sphere An Introduction written by Kendall Atkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-17 with Mathematics categories.
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1987
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Aeronautics categories.
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.
Numerical Methods For Wave Equations In Geophysical Fluid Dynamics
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Author : Dale R. Durran
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Numerical Methods For Wave Equations In Geophysical Fluid Dynamics written by Dale R. Durran and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIlas the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in AppliedMathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and en courage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the AppliedMathematical Sei ences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface This book is designed to serve as a textbook for graduate students or advanced undergraduates studying numerical methods for the solution of partial differen tial equations goveming wave-like flows. Although the majority of the schemes presented in this text were introduced ineither the applied-rnathematics or atmos pheric-science literature, the focus is not on the nuts-and-bolts details of various atmospheric models but on fundamental numerical methods that have applications in a wide range of scientific and engineering disciplines.
Computational Methods In Catalysis And Materials Science
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Author : Rutger A. van Santen
language : en
Publisher: John Wiley & Sons
Release Date : 2015-11-19
Computational Methods In Catalysis And Materials Science written by Rutger A. van Santen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Technology & Engineering categories.
This practical guide describes the basic computational methodologies for catalysis and materials science at an introductory level, presenting the methods with relevant applications, such as spectroscopic properties, chemical reactivity and transport properties of catalytically interesting materials. Edited and authored by internationally recognized scientists, the text provides examples that may be considered and followed as state-of-the art.
Computational Methods In Solid State Physics
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Author : V V Nemoshkalenko
language : en
Publisher: CRC Press
Release Date : 1999-02-19
Computational Methods In Solid State Physics written by V V Nemoshkalenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-19 with Science categories.
The combination of theoretical physics methods, numerical mathematics and computers has given rise to a new field of physics known as "computational physics." The purpose of this monograph is to present the various methods of computational physics, in particular the methods of band theory. The first chapter of the book provides an introduction to the field and presents the theoretical foundations of band theory. In the second and third chapters the authors describe both traditional and more modern methods of band theory and include practical recommendations for their use. Methods which are discussed include APW (augmented plane wave), Green's function method, LMTO (linear method of MT- orbitals), LKKR (linear Korringer, Kohn and Rostocker method), LAPW (linear augmented plane wave), ASW (augmented spherical waves), and LASO (linear method of augmented Slater orbitals). Great attention is paid to the practical aspects of these theories and the book is structured in such a way as to enable the reader to use any method in practice without reference to other sources.
Constructive Approximation On The Sphere With Applications To Geomathematics
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Author : W. Freeden
language : en
Publisher:
Release Date : 1998
Constructive Approximation On The Sphere With Applications To Geomathematics written by W. Freeden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this book provides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area.This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines and wavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to new structures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.
Geometrical Theory Of Satellite Orbits And Gravity Field
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Author : Drazen Svehla
language : en
Publisher: Springer
Release Date : 2018-07-02
Geometrical Theory Of Satellite Orbits And Gravity Field written by Drazen Svehla and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-02 with Science categories.
This book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.
Iutam Symposium On Computational Methods For Unbounded Domains
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Author : Thomas L. Geers
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-10-31
Iutam Symposium On Computational Methods For Unbounded Domains written by Thomas L. Geers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-31 with Technology & Engineering categories.
This volume constitutes the proceedings of the 1997 IUTAM Symposium, where invited researchers in acoustics, aeronautics, elastodynamics, electromagnetics, hydrodynamics, and mathematics discussed non-reflecting computational boundaries. The participants formulated benchmark problems for evaluating computational boundaries, as described in the first article.