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Uncertainty Quantification For Wave Propagation And Flow Problems With Random Data
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Book Synopsis Uncertainty quantification for wave propagation and flow problems with random data by : Markus Wahlsten
Download or read book Uncertainty quantification for wave propagation and flow problems with random data written by Markus Wahlsten and published by Linköping University Electronic Press. This book was released on 2018-04-09 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cardiovascular Mathematics by : Luca Formaggia
Download or read book Cardiovascular Mathematics written by Luca Formaggia and published by Springer Science & Business Media. This book was released on 2010-06-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Book Synopsis Particle Image Velocimetry by : Ronald J. Adrian
Download or read book Particle Image Velocimetry written by Ronald J. Adrian and published by Cambridge University Press. This book was released on 2011 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Particle image velocimetry, or PIV, refers to a class of methods used in experimental fluid mechanics to determine instantaneous fields of the vector velocity by measuring the displacements of numerous fine particles that accurately follow the motion of the fluid. Although the concept of measuring particle displacements is simple in essence, the factors that need to be addressed to design and implement PIV systems that achieve reliable, accurate, and fast measurements and to interpret the results are surprisingly numerous. The aim of this book is to analyze and explain them comprehensively.
Book Synopsis Handbook of Uncertainty Quantification by : Roger Ghanem
Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by Springer. This book was released on 2016-05-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.
Download or read book 2018 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2020-04-07 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Book Synopsis Uncertainty Quantification in Computational Fluid Dynamics by : Hester Bijl
Download or read book Uncertainty Quantification in Computational Fluid Dynamics written by Hester Bijl and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid flows are characterized by uncertain inputs such as random initial data, material and flux coefficients, and boundary conditions. The current volume addresses the pertinent issue of efficiently computing the flow uncertainty, given this initial randomness. It collects seven original review articles that cover improved versions of the Monte Carlo method (the so-called multi-level Monte Carlo method (MLMC)), moment-based stochastic Galerkin methods and modified versions of the stochastic collocation methods that use adaptive stencil selection of the ENO-WENO type in both physical and stochastic space. The methods are also complemented by concrete applications such as flows around aerofoils and rockets, problems of aeroelasticity (fluid-structure interactions), and shallow water flows for propagating water waves. The wealth of numerical examples provide evidence on the suitability of each proposed method as well as comparisons of different approaches.
Book Synopsis Numerical Analysis of Multiscale Problems by : Ivan G. Graham
Download or read book Numerical Analysis of Multiscale Problems written by Ivan G. Graham and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.
Book Synopsis High Order Nonlinear Numerical Schemes for Evolutionary PDEs by : Rémi Abgrall
Download or read book High Order Nonlinear Numerical Schemes for Evolutionary PDEs written by Rémi Abgrall and published by Springer. This book was released on 2014-05-19 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Book Synopsis Active Subspaces by : Paul G. Constantine
Download or read book Active Subspaces written by Paul G. Constantine and published by SIAM. This book was released on 2015-03-17 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
Book Synopsis Uncertainty Quantification in Multiscale Materials Modeling by : Yan Wang
Download or read book Uncertainty Quantification in Multiscale Materials Modeling written by Yan Wang and published by Woodhead Publishing. This book was released on 2020-03-12 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.
Book Synopsis Annual Research Briefs ... by : Center for Turbulence Research (U.S.)
Download or read book Annual Research Briefs ... written by Center for Turbulence Research (U.S.) and published by . This book was released on 2009 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Hydraulic Transients by : Eugen Ruus
Download or read book Applied Hydraulic Transients written by Eugen Ruus and published by Kelowna, B.C. : Ruus Consulting. This book was released on 1997 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Monte Carlo Methods by : Dirk P. Kroese
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Book Synopsis Topics in Modal Analysis, Volume 7 by : Randall Allemang
Download or read book Topics in Modal Analysis, Volume 7 written by Randall Allemang and published by Springer Science & Business Media. This book was released on 2013-07-03 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Modal Analysis, Volume 7: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the seventh volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Fluid Structure Interaction Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data
Book Synopsis Advances in Visualization and Optimization Techniques for Multidisciplinary Research by : Dean Vucinic
Download or read book Advances in Visualization and Optimization Techniques for Multidisciplinary Research written by Dean Vucinic and published by Springer Nature. This book was released on 2019-09-27 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents several multidisciplinary approaches to the visual representation of data acquired from experiments. As an expansion of these approaches, it is also possible to include data examination generated by mathematical-physical modeling. Imaging Systems encompass any subject related to digital images, from fundamental requirements for a correct image acquisition to computational algorithms that make it possible to obtain relevant information for image analysis. In this context, the book presents selected contributions of a special session at the Conference on Advanced Computational Engineering and Experimenting (ACE-X) 2016.
Book Synopsis Stochastic Transport in Upper Ocean Dynamics II by : Bertrand Chapron
Download or read book Stochastic Transport in Upper Ocean Dynamics II written by Bertrand Chapron and published by Springer Nature. This book was released on 2023-11-04 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.
Book Synopsis High Resolution Imaging in Microscopy and Ophthalmology by : Josef F. Bille
Download or read book High Resolution Imaging in Microscopy and Ophthalmology written by Josef F. Bille and published by Springer. This book was released on 2019-08-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a comprehensive overview of the application of the newest laser and microscope/ophthalmoscope technology in the field of high resolution imaging in microscopy and ophthalmology. Starting by describing High-Resolution 3D Light Microscopy with STED and RESOLFT, the book goes on to cover retinal and anterior segment imaging and image-guided treatment and also discusses the development of adaptive optics in vision science and ophthalmology. Using an interdisciplinary approach, the reader will learn about the latest developments and most up to date technology in the field and how these translate to a medical setting. High Resolution Imaging in Microscopy and Ophthalmology – New Frontiers in Biomedical Optics has been written by leading experts in the field and offers insights on engineering, biology, and medicine, thus being a valuable addition for scientists, engineers, and clinicians with technical and medical interest who would like to understand the equipment, the applications and the medical/biological background. Lastly, this book is dedicated to the memory of Dr. Gerhard Zinser, co-founder of Heidelberg Engineering GmbH, a scientist, a husband, a brother, a colleague, and a friend.
