Sparse Grids And Applications Miami 2016

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Sparse Grids and Applications - Miami 2016

Jochen Garcke,Dirk Pflüger,Clayton G. Webster,Guannan Zhang
Sparse Grids and Applications Miami 2016 Book PDF

Author : Jochen Garcke,Dirk Pflüger,Clayton G. Webster,Guannan Zhang
Publisher : Springer
Page : 262 pages
File Size : 40,9 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319754260

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Sparse Grids and Applications - Miami 2016 by Jochen Garcke,Dirk Pflüger,Clayton G. Webster,Guannan Zhang Pdf

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fourth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few.

Sparse Grids and Applications - Munich 2018

Hans-Joachim Bungartz,Jochen Garcke,Dirk Pflüger
Sparse Grids and Applications Munich 2018 Book PDF

Author : Hans-Joachim Bungartz,Jochen Garcke,Dirk Pflüger
Publisher : Springer Nature
Page : 268 pages
File Size : 45,5 Mb
Release : 2022-03-14
Category : Mathematics
ISBN : 9783030813628

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Sparse Grids and Applications - Munich 2018 by Hans-Joachim Bungartz,Jochen Garcke,Dirk Pflüger Pdf

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.

Vibrational Dynamics Of Molecules

Joel M Bowman
Vibrational Dynamics Of Molecules Book PDF

Author : Joel M Bowman
Publisher : World Scientific
Page : 603 pages
File Size : 54,8 Mb
Release : 2022-06-14
Category : Science
ISBN : 9789811237928

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Vibrational Dynamics Of Molecules by Joel M Bowman Pdf

Vibrational Dynamics of Molecules represents the definitive concise text on the cutting-edge field of vibrational molecular chemistry. The chapter contributors are a Who's Who of world leaders in the field. The editor, Joel Bowman, is widely considered as one of the founding fathers of theoretical reaction dynamics. The included topics span the field, from fundamental theory such as collocation methods and vibrational CI methods, to interesting applications such as astrochemistry, supramolecular systems and virtual computational spectroscopy. This is a useful reference for theoretical chemists, spectroscopists, physicists, undergraduate and graduate students, lecturers and software developers.

Software for Exascale Computing - SPPEXA 2016-2019

Hans-Joachim Bungartz,Severin Reiz,Benjamin Uekermann,Philipp Neumann,Wolfgang E. Nagel
Software for Exascale Computing SPPEXA 2016 2019 Book PDF

Author : Hans-Joachim Bungartz,Severin Reiz,Benjamin Uekermann,Philipp Neumann,Wolfgang E. Nagel
Publisher : Springer Nature
Page : 624 pages
File Size : 44,9 Mb
Release : 2020-07-30
Category : Computers
ISBN : 9783030479565

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Software for Exascale Computing - SPPEXA 2016-2019 by Hans-Joachim Bungartz,Severin Reiz,Benjamin Uekermann,Philipp Neumann,Wolfgang E. Nagel Pdf

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

Numerical Geometry, Grid Generation and Scientific Computing

Vladimir A. Garanzha,Lennard Kamenski,Hang Si
Numerical Geometry Grid Generation and Scientific Computing Book PDF

Author : Vladimir A. Garanzha,Lennard Kamenski,Hang Si
Publisher : Springer Nature
Page : 419 pages
File Size : 40,8 Mb
Release : 2021-09-25
Category : Mathematics
ISBN : 9783030767983

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Numerical Geometry, Grid Generation and Scientific Computing by Vladimir A. Garanzha,Lennard Kamenski,Hang Si Pdf

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Sparse Polynomial Approximation of High-Dimensional Functions

Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster
Sparse Polynomial Approximation of High Dimensional Functions Book PDF

Author : Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster
Publisher : SIAM
Page : 310 pages
File Size : 52,8 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9781611976885

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Sparse Polynomial Approximation of High-Dimensional Functions by Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster Pdf

Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Numerical Mathematics and Advanced Applications ENUMATH 2019

Fred J. Vermolen,Cornelis Vuik
Numerical Mathematics and Advanced Applications ENUMATH 2019 Book PDF

Author : Fred J. Vermolen,Cornelis Vuik
Publisher : Springer Nature
Page : 1185 pages
File Size : 52,8 Mb
Release : 2021-04-30
Category : Mathematics
ISBN : 9783030558741

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Numerical Mathematics and Advanced Applications ENUMATH 2019 by Fred J. Vermolen,Cornelis Vuik Pdf

This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

Felix Fritzen,David Ryckelynck
Machine Learning Low Rank Approximations and Reduced Order Modeling in Computational Mechanics Book PDF

Author : Felix Fritzen,David Ryckelynck
Publisher : MDPI
Page : 254 pages
File Size : 47,7 Mb
Release : 2019-09-18
Category : Technology & Engineering
ISBN : 9783039214099

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by Felix Fritzen,David Ryckelynck Pdf

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

TMS 2022 151st Annual Meeting & Exhibition Supplemental Proceedings

The Minerals, Metals & Materials Society
TMS 2022 151st Annual Meeting Exhibition Supplemental Proceedings Book PDF

Author : The Minerals, Metals & Materials Society
Publisher : Springer Nature
Page : 1597 pages
File Size : 55,5 Mb
Release : 2022-03-11
Category : Technology & Engineering
ISBN : 9783030923815

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TMS 2022 151st Annual Meeting & Exhibition Supplemental Proceedings by The Minerals, Metals & Materials Society Pdf

This collection presents papers from the 151st Annual Meeting & Exhibition of The Minerals, Metals & Materials Society.

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Francis X. Giraldo
An Introduction to Element Based Galerkin Methods on Tensor Product Bases Book PDF

Author : Francis X. Giraldo
Publisher : Springer Nature
Page : 559 pages
File Size : 52,8 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030550691

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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases by Francis X. Giraldo Pdf

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Exercises in Numerical Linear Algebra and Matrix Factorizations

Tom Lyche,Georg Muntingh,Øyvind Ryan
Exercises in Numerical Linear Algebra and Matrix Factorizations Book PDF

Author : Tom Lyche,Georg Muntingh,Øyvind Ryan
Publisher : Springer Nature
Page : 265 pages
File Size : 47,5 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9783030597894

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Exercises in Numerical Linear Algebra and Matrix Factorizations by Tom Lyche,Georg Muntingh,Øyvind Ryan Pdf

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 52,6 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Quantification of Uncertainty: Improving Efficiency and Technology

Marta D'Elia,Max Gunzburger,Gianluigi Rozza
Quantification of Uncertainty Improving Efficiency and Technology Book PDF

Author : Marta D'Elia,Max Gunzburger,Gianluigi Rozza
Publisher : Springer Nature
Page : 290 pages
File Size : 47,6 Mb
Release : 2020-07-30
Category : Mathematics
ISBN : 9783030487218

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Quantification of Uncertainty: Improving Efficiency and Technology by Marta D'Elia,Max Gunzburger,Gianluigi Rozza Pdf

This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book’s content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.

DUNE — The Distributed and Unified Numerics Environment

Oliver Sander
DUNE The Distributed and Unified Numerics Environment Book PDF

Author : Oliver Sander
Publisher : Springer Nature
Page : 616 pages
File Size : 42,7 Mb
Release : 2020-12-07
Category : Computers
ISBN : 9783030597023

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DUNE — The Distributed and Unified Numerics Environment by Oliver Sander Pdf

The Distributed and Unified Numerics Environment (Dune) is a set of open-source C++ libraries for the implementation of finite element and finite volume methods. Over the last 15 years it has become one of the most commonly used libraries for the implementation of new, efficient simulation methods in science and engineering. Describing the main Dune libraries in detail, this book covers access to core features like grids, shape functions, and linear algebra, but also higher-level topics like function space bases and assemblers. It includes extensive information on programmer interfaces, together with a wealth of completed examples that illustrate how these interfaces are used in practice. After having read the book, readers will be prepared to write their own advanced finite element simulators, tapping the power of Dune to do so.

Numerical Mathematics and Advanced Applications ENUMATH 2017

Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Numerical Mathematics and Advanced Applications ENUMATH 2017 Book PDF

Author : Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Publisher : Springer
Page : 1070 pages
File Size : 42,5 Mb
Release : 2019-01-05
Category : Computers
ISBN : 9783319964157

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Numerical Mathematics and Advanced Applications ENUMATH 2017 by Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop Pdf

This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).