Tensor Numerical Methods in Scientific Computing PDF Download

Author: Boris N. Khoromskij
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311036591X
Category : Mathematics
Languages : en
Pages : 382

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Book Description
The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

Author: Venera Khoromskaia
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110365839
Category : Mathematics
Languages : en
Pages : 298

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Book Description
The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.

Author: International Union of Pure and Applied Chemistry. Physical and Biophysical Chemistry Division
Publisher: Royal Society of Chemistry
ISBN: 0854044337
Category : Reference
Languages : en
Pages : 240

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Book Description
Prepared by the IUPAC Physical Chemistry Division this definitive manual, now in its third edition, is designed to improve the exchange of scientific information among the readers in different disciplines and across different nations. This book has been systematically brought up to date and new sections added to reflect the increasing volume of scientific literature and terminology and expressions being used. The Third Edition reflects the experience of the contributors with the previous editions and the comments and feedback have been integrated into this essential resource. This edition has been compiled in machine-readable form and will be available online.

Author: James Binney
Publisher: Oxford University Press, USA
ISBN: 0199688575
Category : Science
Languages : en
Pages : 408

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Book Description
This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.

Author: Ian David Brown
Publisher:
ISBN: 0198508700
Category : Science
Languages : en
Pages : 289

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Book Description
This book describes the bond valence model, a description of acid-base bonding which is becoming increasingly popular particularly in fields such as materials science and mineralogy where solid state inorganic chemistry is important. Recent improvements in crystal structure determination have allowed the model to become more quantitative. Unlike other models of inorganic chemical bonding, the bond valence model is simple, intuitive, and predictive, and can be used for analysing crystal structures and the conceptual modelling of local as well as extended structures. This is the first book to explore in depth the theoretical basis of the model and to show how it can be applied to synthetic and solution chemistry. It emphasizes the separate roles of the constraints of chemistry and of three-dimensional space by analysing the chemistry of solids. Many applications of the model in physics, materials science, chemistry, mineralogy, soil science, surface science, and molecular biology are reviewed. The final chapter describes how the bond valence model relates to and represents a simplification of other models of inorganic chemical bonding.

Author: Frederick Wooten
Publisher: Academic Press
ISBN: 1483220761
Category : Science
Languages : en
Pages : 273

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Book Description
Optical Properties of Solids covers the important concepts of intrinsic optical properties and photoelectric emission. The book starts by providing an introduction to the fundamental optical spectra of solids. The text then discusses Maxwell's equations and the dielectric function; absorption and dispersion; and the theory of free-electron metals. The quantum mechanical theory of direct and indirect transitions between bands; the applications of dispersion relations; and the derivation of an expression for the dielectric function in the self-consistent field approximation are also encompassed. The book further tackles current-current correlations; the fluctuation-dissipation theorem; and the effect of surface plasmons on optical properties and photoemission. People involved in the study of the optical properties of solids will find the book invaluable.

Author: Zi-Kui Liu
Publisher: Cambridge University Press
ISBN: 0521198968
Category : Science
Languages : en
Pages : 261

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Book Description
Integrates fundamental concepts with experimental data and practical applications, including worked examples and end-of-chapter problems.

Author: P.-A. Absil
Publisher: Princeton University Press
ISBN: 1400830249
Category : Mathematics
Languages : en
Pages : 240

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Book Description
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

Author: D. R. Yarkony
Publisher: World Scientific
ISBN: 9812832114
Category : Science
Languages : en
Pages : 785

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Book Description
Modern Electronic Structure Theory provides a didactically oriented description of the latest computational techniques in electronic structure theory and their impact in several areas of chemistry. The book is aimed at first year graduate students or college seniors considering graduate study in computational chemistry, or researchers who wish to acquire a wider knowledge of this field.

Author: T. Sheppard
Publisher: Springer Science & Business Media
ISBN: 1475730012
Category : Technology & Engineering
Languages : en
Pages : 428

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Book Description
In recent years the importance of extruded alloys has increased due to the decline in copper extrusion, increased use in structural applications, environmental impact and reduced energy consumption. There have also been huge technical advances. This text provides comprehensive coverage of the metallurgical, mathematical and practical features of the process.