Polynomial Chaos Methods for Hyperbolic Partial Differential Equations PDF Download
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Author: Mass Per Pettersson
Publisher: Springer
ISBN: 3319107143
Category : Technology & Engineering
Languages : en
Pages : 217
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Book Description
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.
Author: Mass Per Pettersson
Publisher: Springer
ISBN: 3319107143
Category : Technology & Engineering
Languages : en
Pages : 217
Get Book Here
Book Description
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.
Author: Giacomo Albi
Publisher: Springer Nature
ISBN: 3031298756
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
Author: Jens M. Melenk
Publisher: Springer Nature
ISBN: 3031204328
Category : Mathematics
Languages : en
Pages : 571
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Book Description
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.
Author: Christian Klingenberg
Publisher: Springer
ISBN: 3319915487
Category : Mathematics
Languages : en
Pages : 698
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Book Description
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.
Author: Shi Jin
Publisher: Springer
ISBN: 3319671103
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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.
Author: Christos Christopoulos
Publisher: CRC Press
ISBN: 1000631788
Category : Technology & Engineering
Languages : en
Pages : 658
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Book Description
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.
Author: Charles Hirsch
Publisher: Springer
ISBN: 331977767X
Category : Technology & Engineering
Languages : en
Pages : 799
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Book Description
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.
Author: Markus Wahlsten
Publisher: Linköping University Electronic Press
ISBN: 917685339X
Category :
Languages : en
Pages : 45
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Book Description
In this thesis we study partial differential equations with random inputs. The effects that different boundary conditions with random data and uncertain geometries have on the solution are analyzed. Further, comparisons and couplings between different uncertainty quantification methods are performed. The numerical simulations are based on provably strongly stable finite difference formulations based on summation-by-parts operators and a weak implementation of boundary and interface conditions. The first part of this thesis treats the construction of variance reducing boundary conditions. It is shown how the variance of the solution can be manipulated by the choice of boundary conditions, and a close relation between the variance of the solution and the energy estimate is established. The technique is studied on both a purely hyperbolic system as well as an incompletely parabolic system of equations. The applications considered are the Euler, Maxwell's, and Navier--Stokes equations. The second part focuses on the effect of uncertain geometry on the solution. We consider a two-dimensional advection-diffusion equation with a stochastically varying boundary. We transform the problem to a fixed domain where comparisons can be made. Numerical results are performed on a problem in heat transfer, where the frequency and amplitude of the prescribed uncertainty are varied. The final part of the thesis is devoted to the comparison and coupling of different uncertainty quantification methods. An efficiency analysis is performed using the intrusive polynomial chaos expansion with stochastic Galerkin projection, and nonintrusive numerical integration. The techniques are compared using the non-linear viscous Burgers' equation. A provably stable coupling procedure for the two methods is also constructed. The general coupling procedure is exemplified using a hyperbolic system of equations.
Author: Flavio Canavero
Publisher: Springer
ISBN: 3030048705
Category : Technology & Engineering
Languages : en
Pages : 186
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Book Description
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.
Author: Stephen Ekwaro-Osire
Publisher: Springer
ISBN: 3319558528
Category : Technology & Engineering
Languages : en
Pages : 273
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Book Description
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.
