Finite Element Exterior Calculus

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Finite Element Exterior Calculus

Douglas N. Arnold
Finite Element Exterior Calculus Book PDF

Author : Douglas N. Arnold
Publisher : SIAM
Page : 126 pages
File Size : 46,5 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781611975536

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Finite Element Exterior Calculus by Douglas N. Arnold Pdf

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world?wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more?are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

Finite Element Exterior Calculus

Douglas N. Arnold
Finite Element Exterior Calculus Book PDF

Author : Douglas N. Arnold
Publisher : SIAM
Page : 120 pages
File Size : 50,9 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781611975543

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Finite Element Exterior Calculus by Douglas N. Arnold Pdf

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world—wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more—are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

Computational Electromagnetism

Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez
Computational Electromagnetism Book PDF

Author : Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez
Publisher : Springer
Page : 240 pages
File Size : 50,7 Mb
Release : 2015-07-20
Category : Mathematics
ISBN : 9783319193069

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Computational Electromagnetism by Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez Pdf

Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.

The Finite Element Method: Theory, Implementation, and Applications

Mats G. Larson,Fredrik Bengzon
The Finite Element Method Theory Implementation and Applications Book PDF

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 49,6 Mb
Release : 2013-01-13
Category : Computers
ISBN : 9783642332876

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The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Numerical Solution of Partial Differential Equations by the Finite Element Method

Claes Johnson
Numerical Solution of Partial Differential Equations by the Finite Element Method Book PDF

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 43,5 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Automated Solution of Differential Equations by the Finite Element Method

Anders Logg,Kent-Andre Mardal,Garth Wells
Automated Solution of Differential Equations by the Finite Element Method Book PDF

Author : Anders Logg,Kent-Andre Mardal,Garth Wells
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 52,7 Mb
Release : 2012-02-24
Category : Computers
ISBN : 9783642230998

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Automated Solution of Differential Equations by the Finite Element Method by Anders Logg,Kent-Andre Mardal,Garth Wells Pdf

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Finite Element Methods for Computational Fluid Dynamics

Dmitri Kuzmin,Jari Hamalainen
Finite Element Methods for Computational Fluid Dynamics Book PDF

Author : Dmitri Kuzmin,Jari Hamalainen
Publisher : SIAM
Page : 321 pages
File Size : 45,7 Mb
Release : 2014-12-18
Category : Science
ISBN : 9781611973600

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Finite Element Methods for Computational Fluid Dynamics by Dmitri Kuzmin,Jari Hamalainen Pdf

This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?

Finite Element Methods for Maxwell's Equations

Peter Monk
Finite Element Methods for Maxwell s Equations Book PDF

Author : Peter Monk
Publisher : Clarendon Press
Page : 468 pages
File Size : 46,5 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 9780191545221

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Finite Element Methods for Maxwell's Equations by Peter Monk Pdf

Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.

Crystal Plasticity Finite Element Methods

Franz Roters,Philip Eisenlohr,Thomas R. Bieler,Dierk Raabe
Crystal Plasticity Finite Element Methods Book PDF

Author : Franz Roters,Philip Eisenlohr,Thomas R. Bieler,Dierk Raabe
Publisher : John Wiley & Sons
Page : 188 pages
File Size : 52,8 Mb
Release : 2011-08-04
Category : Technology & Engineering
ISBN : 9783527642090

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Crystal Plasticity Finite Element Methods by Franz Roters,Philip Eisenlohr,Thomas R. Bieler,Dierk Raabe Pdf

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.

Acta Numerica 2010: Volume 19

Arieh Iserles
Acta Numerica 2010 Volume 19 Book PDF

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 614 pages
File Size : 42,8 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 0521192846

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Acta Numerica 2010: Volume 19 by Arieh Iserles Pdf

A high-impact, prestigious, annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Mathematical Foundations of Finite Elements and Iterative Solvers

SCI085000
Mathematical Foundations of Finite Elements and Iterative Solvers Book PDF

Author : SCI085000
Publisher : SIAM
Page : 186 pages
File Size : 45,6 Mb
Release : 2022-06-27
Category : Mathematics
ISBN : 9781611977097

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Mathematical Foundations of Finite Elements and Iterative Solvers by SCI085000 Pdf

“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.

Compatible Spatial Discretizations

Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov
Compatible Spatial Discretizations Book PDF

Author : Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 52,6 Mb
Release : 2007-01-26
Category : Mathematics
ISBN : 9780387380346

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Compatible Spatial Discretizations by Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov Pdf

The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.

Mixed Finite Element Methods and Applications

Daniele Boffi,Franco Brezzi,Michel Fortin
Mixed Finite Element Methods and Applications Book PDF

Author : Daniele Boffi,Franco Brezzi,Michel Fortin
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 50,8 Mb
Release : 2013-07-02
Category : Mathematics
ISBN : 9783642365195

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Mixed Finite Element Methods and Applications by Daniele Boffi,Franco Brezzi,Michel Fortin Pdf

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.

Transport Processes at Fluidic Interfaces

Dieter Bothe,Arnold Reusken
Transport Processes at Fluidic Interfaces Book PDF

Author : Dieter Bothe,Arnold Reusken
Publisher : Birkhäuser
Page : 679 pages
File Size : 54,8 Mb
Release : 2017-07-13
Category : Mathematics
ISBN : 9783319566023

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Transport Processes at Fluidic Interfaces by Dieter Bothe,Arnold Reusken Pdf

There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”

Advanced Calculus

Lynn Harold Loomis,Shlomo Sternberg
Advanced Calculus Book PDF

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 45,7 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.