Computational Aspects
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Computational Aspects
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Author : Carlos A. Brebbia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12
Computational Aspects written by Carlos A. Brebbia 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 2013-03-12 with Science categories.
Past volumes of this series have concentrated on the theoretical and the more formal aspects of the boundary element method. The present book instead stresses the computational aspects of the technique and its applications with the objective of facilitating the implementation of BEM in the engineering industry and its better understanding in the teaching and research environments. The book starts by discussing the topics of convergence of solutions, application to nonlinear problems and numerical integration. This is followed by a long chapter on the computational aspects of the method, discussing the different numerical schemes and the way in which influence functions can be computed. Three separate chapters deal with important techniques which are related to classical boundary elements, namely the edge method, multigrid schemes and the complex variable boundary element approach. The last two chapters are of special interest as they present and explain in detail two FORTRAN codes which have numerous applications in engineering, i.e. a code for the solution of potential problems and another for elastostatics. Each sub routine in the programs is listed and explained. The codes follow the same format as the ones in the classical book "The Boundary Element Method for Engineers" (by C. A. Brebbia, Computational Mechanics Publications, first published in 1978) but are more advanced in terms of elements and capabilities. In particular the new listings deal with symmetry, linear elements for the two dimensional elasticity, some mixed type of boundary conditions and the treatment of infinite regions.
Shell And Spatial Structures Computational Aspects
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Author : Guido De Roeck
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Shell And Spatial Structures Computational Aspects written by Guido De Roeck 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 2013-03-13 with Science categories.
In recent years powerful engineering workstations for a reasonable price become a valuable tool for the design of complicated constructions such as shell and spatial structures. This availability causes an increasing use of advanced numerical techniques for the static and dynamic analysis of these structures, also in the non-linear range. The I.A.S.S. Working Group nO 13 concerned with "Numerical Methods in Shell and Spatial Structures" and the Department of Civil Engineering of the Katholieke Universiteit Leuven have taken the initiative to organise an International Symposium, providing a forum for discussion and exchange of views between researchers, specialists in numerical analysis on one hand and designers, practising engineer ings on the other hand. These Proceedings contain the papers presented at the Symposium, held in Leuven, July 14-16 1986. The papers are organised in five sections 1. Shell structures 2. Spatial structures 3. Dynamic analysis 4. Non-linear analysis 5. Presentation and interpretation of results The papers covering more than one domain are classified following the main subject. We hope that researchers as well as practising engineers will find a lot of useful information in the book.
Computational Aspects Of Modular Forms And Galois Representations
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Author : Bas Edixhoven
language : en
Publisher: Princeton University Press
Release Date : 2011-06-20
Computational Aspects Of Modular Forms And Galois Representations written by Bas Edixhoven and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-20 with Mathematics categories.
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Mathematical And Computational Aspects
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Author : Carlos A. Brebbia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Mathematical And Computational Aspects written by Carlos A. Brebbia 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 2013-11-21 with Technology & Engineering categories.
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.
Computational Aspects For Large Chemical Systems
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Author : E. Clementi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Aspects For Large Chemical Systems written by E. Clementi 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 2012-12-06 with Science categories.
1. 1 STATEMENT OF THE PROBLEM Quantum chemistry judged not from the ever present possibility of unex pected developments but on the basis of the achievements in the last fifty years, is predominantly limited to attempts to solve for the energy and expectation values of wave functions representing, in the limit, an exact solution to the Schroedinger equation. Because of well-known dif ficulties in system with more than about 50 electrons, the adopted ap proximations are generally rather crude. As examples of quantum chemical approximations we mention the total or partial neglects of electron correlation, the neglect of relativistic effects, the use of subminimal basis sets, the still present neglect of inner-core electrons in semi-empirical methods, the acceptance of the Born-Oppenheimer approximations, and so on. In general, the larger the system, in terms of the number of electrons, the cruder the approxima tion. In a way, the present status of quantum chemistry might appear as nearly paradoxical. Indeed, for small systems, where very accurate ex periments are often available, and therefore, there is not a great need to obtain (from quantum chemistry) predictions of new data but rather ,a theoretical interpretation of the existing data, we find increasi~gly powerful and reliable quantum chemical methods and techniques.
Computational Aspects Of Penetration Mechanics
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Author : J. Chandra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Aspects Of Penetration Mechanics written by J. Chandra 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 2012-12-06 with Science categories.
Physical And Computational Aspects Of Convective Heat Transfer
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Author : Tuncer Cebeci
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Physical And Computational Aspects Of Convective Heat Transfer written by Tuncer Cebeci 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 2012-12-06 with Science categories.
From the reviews: "The book has a broad and general coverage of both the mathematics and the numerical methods well suited for graduate students." Applied Mechanics Reviews #1 "This is a very well written book. The topics are developed with separate headings making the matter easily understandable. Computer programs are also included for many problems together with a separate chapter dealing with the application of computer programs to heat transfer problems. This enhances the utility of the book." Zentralblatt für Mathematik #1
Computational Aspects Of Discrete Subgroups Of Lie Groups
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Author : Alla Detinko
language : en
Publisher: American Mathematical Society
Release Date : 2023-03-10
Computational Aspects Of Discrete Subgroups Of Lie Groups written by Alla Detinko and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-10 with Mathematics categories.
This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.
Computational Aspects Of Electric Polarizability Calculations
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Author : George Maroulis
language : en
Publisher: IOS Press
Release Date : 2006
Computational Aspects Of Electric Polarizability Calculations written by George Maroulis and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
Covers such subjects as: Ab initio and Density functional theory calculations of electric polarizability and hyperpolarizability, intermolecular forces, aromaticity, electric properties of solvated molecules, NLO materials, Raman intensities, polarizability of metal and semiconductor clusters, relativistic effects on electric properties, and more.
Nonparametric Kernel Density Estimation And Its Computational Aspects
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Author : Artur Gramacki
language : en
Publisher: Springer
Release Date : 2017-12-21
Nonparametric Kernel Density Estimation And Its Computational Aspects written by Artur Gramacki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Technology & Engineering categories.
This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.