Mathematical Foundations Of Finite Elements And Iterative Solvers
DOWNLOAD
Download Mathematical Foundations Of Finite Elements And Iterative Solvers PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Mathematical Foundations Of Finite Elements And Iterative Solvers book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Mathematical Foundations Of Finite Elements And Iterative Solvers
DOWNLOAD
Author : Paolo Gatto
language : en
Publisher: SIAM
Release Date : 2022-06-27
Mathematical Foundations Of Finite Elements And Iterative Solvers written by Paolo Gatto and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-27 with Mathematics categories.
“This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together.” — Richard S. Falk, Rutgers University “Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style.” — J. Tinsley Oden, The University of Texas at Austin This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.
Mathematical Theory Of Finite Elements
DOWNLOAD
Author : Leszek F. Demkowicz
language : en
Publisher: SIAM
Release Date : 2023-09-22
Mathematical Theory Of Finite Elements written by Leszek F. Demkowicz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-22 with Mathematics categories.
This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
Enhanced Introduction To Finite Elements For Engineers
DOWNLOAD
Author : Uwe Mühlich
language : en
Publisher: Springer Nature
Release Date : 2023-05-31
Enhanced Introduction To Finite Elements For Engineers written by Uwe Mühlich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Science categories.
The book presents the fundamentals of the Galerkin Finite Element Method for linear boundary value problems from an engineering perspective. Emphasis is given to the theoretical foundation of the method rooted in Functional Analysis using a language accessible to engineers. The book discusses standard procedures for applying the method to time-dependent and nonlinear problems and addresses essential aspects of applying the method to non-linear dynamics and multi-physics problems. It also provides several hand-calculation exercises as well as specific computer exercises with didactic character. About one fourth of the exercises reveals common pitfalls and sources of errors when applying the method. Carefully selected literature recommendations for further studies are provided at the end of each chapter. The reader is expected to have prior knowledge in engineering mathematics, in particular real analysis and linear algebra. The elements of algebra and analysis required in the main part of the book are presented in corresponding sections of the appendix. Students should already have an education in strength of materials or another engineering field, such as heat or mass transport, which discusses boundary value problems for simple geometries and boundary conditions.
A First Course In Linear Optimization
DOWNLOAD
Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2025-05-05
A First Course In Linear Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.
This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability to apply the theory and algorithms to actual problems. To deepen the reader’s understanding, the authors provide many applications from diverse areas of applied sciences, such as resource allocation, line fitting, graph coloring, the traveling salesman problem, game theory, and network flows; more than 180 exercises, most of them with partial answers and about 70 with complete solutions; and a continuous illustration of the theory through examples and exercises. A First Course in Linear Optimization is intended to be read cover to cover and requires only a first course in linear algebra as a prerequisite. Its 13 chapters can be used as lecture notes for a first course in linear optimization. This book is for a first undergraduate course in linear optimization, such as linear programming, linear optimization, and operations research. It is appropriate for students in operations research, mathematics, economics, and industrial engineering, as well as those studying computer science and engineering disciplines.
A Ramble Through Probability
DOWNLOAD
Author : Samopriya Basu
language : en
Publisher: SIAM
Release Date : 2024-03-06
A Ramble Through Probability written by Samopriya Basu and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-06 with Mathematics categories.
Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website. This book is intended for graduate students in engineering, mathematics, science, and statistics. Researchers who need to use probability theory will also find it useful. It is appropriate for graduate-level courses on measure theory and/or probability theory.
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
DOWNLOAD
Author : George Haller
language : en
Publisher: SIAM
Release Date : 2025-05-20
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls written by George Haller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Computers categories.
This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book introduces the foundations of SSM theory to the novice reader; reviews recent extensions of classic SSM results for the advanced reader; and illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control. This book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling.
Implementation Of Finite Element Methods For Navier Stokes Equations
DOWNLOAD
Author : F. Thomasset
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Implementation Of Finite Element Methods For Navier Stokes Equations written by F. Thomasset and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Numerical Partial Differential Equations
DOWNLOAD
Author : James H. Adler
language : en
Publisher: SIAM
Release Date : 2025-03-26
Numerical Partial Differential Equations written by James H. Adler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-26 with Mathematics categories.
This comprehensive textbook focuses on numerical methods for approximating solutions to partial differential equations (PDEs). The authors present a broad survey of these methods, introducing readers to the central concepts of various families of discretizations and solution algorithms and laying the foundation needed to understand more advanced material. The authors include over 100 well-established definitions, theorems, corollaries, and lemmas and summaries of and references to in-depth treatments of more advanced mathematics when needed. Numerical Partial Differential Equations is divided into four parts: Part I covers basic background on PDEs and numerical methods. Part II introduces the three main classes of numerical methods for PDEs that are the book’s focus (finite-difference, finite-element, and finite-volume methods). Part III discusses linear solvers and finite-element and finite-volume methods at a more advanced level. Part IV presents further high-level topics on discretizations and solvers. This book is intended for advanced undergraduate/first-year graduate and advanced graduate students in applied math, as well as students in science and engineering disciplines. The book will also appeal to researchers in the field of scientific computing. Chapters are designed to be stand-alone, allowing distinct paths through the text, making it appropriate for both single-semester and multi-semester courses. It is appropriate for courses covering topics ranging from numerical methods for PDEs to numerical linear algebra.
Uncertainty Quantification
DOWNLOAD
Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2024-09-13
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-13 with Mathematics categories.
Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.
Theoretical Numerical Analysis
DOWNLOAD
Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Theoretical Numerical Analysis written by Kendall Atkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this text book series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs.