Polynomial Chaos Methods For Hyperbolic Partial Differential Equations

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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström
Polynomial Chaos Methods for Hyperbolic Partial Differential Equations Book PDF

Author : Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström
Publisher : Springer
Page : 214 pages
File Size : 54,5 Mb
Release : 2015-03-10
Category : Technology & Engineering
ISBN : 9783319107141

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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations by Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström Pdf

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems

Giacomo Albi,Walter Boscheri,Mattia Zanella
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems Book PDF

Author : Giacomo Albi,Walter Boscheri,Mattia Zanella
Publisher : Springer Nature
Page : 241 pages
File Size : 54,6 Mb
Release : 2023-06-02
Category : Mathematics
ISBN : 9783031298752

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Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems by Giacomo Albi,Walter Boscheri,Mattia Zanella Pdf

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.

Partial Differential Equations of Hyperbolic Type and Applications

Giuseppe Geymonat
Partial Differential Equations of Hyperbolic Type and Applications Book PDF

Author : Giuseppe Geymonat
Publisher : World Scientific
Page : 196 pages
File Size : 48,8 Mb
Release : 1987
Category : Mathematics
ISBN : 9971502054

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Partial Differential Equations of Hyperbolic Type and Applications by Giuseppe Geymonat Pdf

This book introduces the general aspects of hyperbolic conservation laws and their numerical approximation using some of the most modern tools: spectral methods, unstructured meshes and ?-formulation. The applications of these methods are found in some significant examples such as the Euler equations. This book, a collection of articles by the best authors in the field, exposes the reader to the frontier of the research and many open problems.

Uncertainty Quantification for Hyperbolic and Kinetic Equations

Shi Jin,Lorenzo Pareschi
Uncertainty Quantification for Hyperbolic and Kinetic Equations Book PDF

Author : Shi Jin,Lorenzo Pareschi
Publisher : Springer
Page : 277 pages
File Size : 48,9 Mb
Release : 2018-03-20
Category : Mathematics
ISBN : 9783319671109

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Uncertainty Quantification for Hyperbolic and Kinetic Equations by Shi Jin,Lorenzo Pareschi Pdf

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Theory, Numerics and Applications of Hyperbolic Problems II

Christian Klingenberg,Michael Westdickenberg
Theory Numerics and Applications of Hyperbolic Problems II Book PDF

Author : Christian Klingenberg,Michael Westdickenberg
Publisher : Springer
Page : 714 pages
File Size : 43,7 Mb
Release : 2018-06-27
Category : Mathematics
ISBN : 9783319915487

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Theory, Numerics and Applications of Hyperbolic Problems II by Christian Klingenberg,Michael Westdickenberg Pdf

The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Uncertainty Management for Robust Industrial Design in Aeronautics

Charles Hirsch,Dirk Wunsch,Jacek Szumbarski,Łukasz Łaniewski-Wołłk,Jordi Pons-Prats
Uncertainty Management for Robust Industrial Design in Aeronautics Book PDF

Author : Charles Hirsch,Dirk Wunsch,Jacek Szumbarski,Łukasz Łaniewski-Wołłk,Jordi Pons-Prats
Publisher : Springer
Page : 819 pages
File Size : 52,6 Mb
Release : 2018-07-21
Category : Technology & Engineering
ISBN : 9783319777672

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Uncertainty Management for Robust Industrial Design in Aeronautics by Charles Hirsch,Dirk Wunsch,Jacek Szumbarski,Łukasz Łaniewski-Wołłk,Jordi Pons-Prats Pdf

This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations.

Principles and Techniques of Electromagnetic Compatibility

Christos Christopoulos
Principles and Techniques of Electromagnetic Compatibility Book PDF

Author : Christos Christopoulos
Publisher : CRC Press
Page : 658 pages
File Size : 40,8 Mb
Release : 2022-07-14
Category : Technology & Engineering
ISBN : 9781000631784

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Principles and Techniques of Electromagnetic Compatibility by Christos Christopoulos Pdf

This book provides a sound grasp of the fundamental concepts, applications, and practice of EMC. Developments in recent years have resulted in further increases in electrical component density, wider penetration of wireless technologies, and a significant increase in complexity of electrical and electronic equipment. New materials, which can be customized to meet EMC needs, have been introduced. Considerable progress has been made in developing numerical tools for complete system EMC simulation. EMC is now a central consideration in all industrial sectors. Maintaining the holistic approach of the previous edition of Principles and Techniques of Electromagnetic Compatibility, the Third Edition updates coverage of EMC to reflects recent important developments. What is new in the Third Edition? A comprehensive treatment of new materials (meta- and nano-) and their impact on EMC Numerical modelling of complex systems and complexity reduction methods Impact of wireless technologies and the Internet of Things (IoT) on EMC Testing in reverberation chambers, and in the time-domain A comprehensive treatment of the scope and development of stochastic models for EMC EMC issues encountered in automotive, railway, aerospace, and marine applications Impact of EMC and Intentional EMI (IEMI) on infrastructure, and risk assessment In addition to updating material, new references, examples, and appendices were added to offer further support to readers interested in exploring further. As in previous editions, the emphasis is on building a sound theoretical framework, and demonstrating how it can be turned to practical use in challenging applications. The expectation is that this approach will serve EMC engineers through the inevitable future technological shifts and developments.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020 1 Book PDF

Author : Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab
Publisher : Springer Nature
Page : 571 pages
File Size : 49,6 Mb
Release : 2023-06-30
Category : Mathematics
ISBN : 9783031204326

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab Pdf

The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.

Hyperbolic Partial Differential Equations

Peter D. Lax
Hyperbolic Partial Differential Equations Book PDF

Author : Peter D. Lax
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 43,5 Mb
Release : 2006
Category : Differential equations, Hyperbolic
ISBN : 9780821835760

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Hyperbolic Partial Differential Equations by Peter D. Lax Pdf

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Uncertainty Modeling for Engineering Applications

Flavio Canavero
Uncertainty Modeling for Engineering Applications Book PDF

Author : Flavio Canavero
Publisher : Springer
Page : 184 pages
File Size : 51,6 Mb
Release : 2018-12-29
Category : Technology & Engineering
ISBN : 9783030048709

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Uncertainty Modeling for Engineering Applications by Flavio Canavero Pdf

This book provides an overview of state-of-the-art uncertainty quantification (UQ) methodologies and applications, and covers a wide range of current research, future challenges and applications in various domains, such as aerospace and mechanical applications, structure health and seismic hazard, electromagnetic energy (its impact on systems and humans) and global environmental state change. Written by leading international experts from different fields, the book demonstrates the unifying property of UQ theme that can be profitably adopted to solve problems of different domains. The collection in one place of different methodologies for different applications has the great value of stimulating the cross-fertilization and alleviate the language barrier among areas sharing a common background of mathematical modeling for problem solution. The book is designed for researchers, professionals and graduate students interested in quantitatively assessing the effects of uncertainties in their fields of application. The contents build upon the workshop “Uncertainty Modeling for Engineering Applications” (UMEMA 2017), held in Torino, Italy in November 2017.

Probabilistic Prognostics and Health Management of Energy Systems

Stephen Ekwaro-Osire,Aparecido Carlos Gonçalves,Fisseha M. Alemayehu
Probabilistic Prognostics and Health Management of Energy Systems Book PDF

Author : Stephen Ekwaro-Osire,Aparecido Carlos Gonçalves,Fisseha M. Alemayehu
Publisher : Springer
Page : 277 pages
File Size : 41,6 Mb
Release : 2017-04-25
Category : Technology & Engineering
ISBN : 9783319558523

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Probabilistic Prognostics and Health Management of Energy Systems by Stephen Ekwaro-Osire,Aparecido Carlos Gonçalves,Fisseha M. Alemayehu Pdf

This book proposes the formulation of an efficient methodology that estimates energy system uncertainty and predicts Remaining Useful Life (RUL) accurately with significantly reduced RUL prediction uncertainty. Renewable and non-renewable sources of energy are being used to supply the demands of societies worldwide. These sources are mainly thermo-chemo-electro-mechanical systems that are subject to uncertainty in future loading conditions, material properties, process noise, and other design parameters.It book informs the reader of existing and new ideas that will be implemented in RUL prediction of energy systems in the future. The book provides case studies, illustrations, graphs, and charts. Its chapters consider engineering, reliability, prognostics and health management, probabilistic multibody dynamical analysis, peridynamic and finite-element modelling, computer science, and mathematics.

Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws

Philipp Öffner
Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws Book PDF

Author : Philipp Öffner
Publisher : Springer Nature
Page : 486 pages
File Size : 50,9 Mb
Release : 2023-09-17
Category : Mathematics
ISBN : 9783658426200

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Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws by Philipp Öffner Pdf

The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.

Finite Volume Methods for Hyperbolic Problems

Randall J. LeVeque
Finite Volume Methods for Hyperbolic Problems Book PDF

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 496 pages
File Size : 55,9 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 9781139434188

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Multi-dimensional Hyperbolic Partial Differential Equations

Sylvie Benzoni-Gavage,Denis Serre
Multi dimensional Hyperbolic Partial Differential Equations Book PDF

Author : Sylvie Benzoni-Gavage,Denis Serre
Publisher : Oxford University Press on Demand
Page : 535 pages
File Size : 45,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780199211234

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Multi-dimensional Hyperbolic Partial Differential Equations by Sylvie Benzoni-Gavage,Denis Serre Pdf

Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Compressed Sensing and its Applications

Holger Boche,Giuseppe Caire,Robert Calderbank,Maximilian März,Gitta Kutyniok,Rudolf Mathar
Compressed Sensing and its Applications Book PDF

Author : Holger Boche,Giuseppe Caire,Robert Calderbank,Maximilian März,Gitta Kutyniok,Rudolf Mathar
Publisher : Birkhäuser
Page : 388 pages
File Size : 46,5 Mb
Release : 2018-01-17
Category : Mathematics
ISBN : 9783319698021

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Compressed Sensing and its Applications by Holger Boche,Giuseppe Caire,Robert Calderbank,Maximilian März,Gitta Kutyniok,Rudolf Mathar Pdf

This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.