An Introduction To Element Based Galerkin Methods On Tensor Product Bases

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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Francis X. Giraldo
An Introduction to Element Based Galerkin Methods on Tensor Product Bases Book PDF

Author : Francis X. Giraldo
Publisher : Springer Nature
Page : 559 pages
File Size : 47,9 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030550691

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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases by Francis X. Giraldo Pdf

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 51,5 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

The Finite Element Method: Its Basis and Fundamentals

Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu
The Finite Element Method Its Basis and Fundamentals Book PDF

Author : Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu
Publisher : Elsevier
Page : 752 pages
File Size : 55,8 Mb
Release : 2005-05-26
Category : Technology & Engineering
ISBN : 008047277X

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The Finite Element Method: Its Basis and Fundamentals by Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu Pdf

The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
Certified Reduced Basis Methods for Parametrized Partial Differential Equations Book PDF

Author : Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
Publisher : Springer
Page : 131 pages
File Size : 45,6 Mb
Release : 2015-08-20
Category : Mathematics
ISBN : 9783319224701

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations by Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm Pdf

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

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 : 42,5 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.

Pragmatic Introduction To The Finite Element Method For Thermal And Stress Analysis, A: With The Matlab Toolkit Sofea

Petr Krysl
Pragmatic Introduction To The Finite Element Method For Thermal And Stress Analysis A With The Matlab Toolkit Sofea Book PDF

Author : Petr Krysl
Publisher : World Scientific Publishing Company
Page : 292 pages
File Size : 45,8 Mb
Release : 2006-10-23
Category : Science
ISBN : 9789813101814

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Pragmatic Introduction To The Finite Element Method For Thermal And Stress Analysis, A: With The Matlab Toolkit Sofea by Petr Krysl Pdf

This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab.The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions; the method of weighted residuals is applied to derive the discrete equations; and clear examples are introduced to illustrate the method.

Discontinuous Galerkin Methods

Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Discontinuous Galerkin Methods Book PDF

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642597213

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Discontinuous Galerkin Methods by Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu Pdf

A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Chebyshev and Fourier Spectral Methods

John P. Boyd
Chebyshev and Fourier Spectral Methods Book PDF

Author : John P. Boyd
Publisher : Courier Corporation
Page : 690 pages
File Size : 55,9 Mb
Release : 2001-12-03
Category : Mathematics
ISBN : 9780486411835

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Chebyshev and Fourier Spectral Methods by John P. Boyd Pdf

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Numerical Methods in Turbulence Simulation

Robert Moser
Numerical Methods in Turbulence Simulation Book PDF

Author : Robert Moser
Publisher : Elsevier
Page : 568 pages
File Size : 54,9 Mb
Release : 2022-11-30
Category : Science
ISBN : 9780323998338

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Numerical Methods in Turbulence Simulation by Robert Moser Pdf

Numerical Methods in Turbulence Simulation provides detailed specifications of the numerical methods needed to solve important problems in turbulence simulation. Numerical simulation of turbulent fluid flows is challenging because of the range of space and time scales that must be represented. This book provides explanations of the numerical error and stability characteristics of numerical techniques, along with treatments of the additional numerical challenges that arise in large eddy simulations. Chapters are written as tutorials by experts in the field, covering specific both contexts and applications. Three classes of turbulent flow are addressed, including incompressible, compressible and reactive, with a wide range of the best numerical practices covered. A thorough introduction to the numerical methods is provided for those without a background in turbulence, as is everything needed for a thorough understanding of the fundamental equations. The small scales that must be resolved are generally not localized around some distinct small-scale feature, but instead are distributed throughout a volume. These characteristics put particular strain on the numerical methods used to simulate turbulent flows. Includes a detailed review of the numerical approximation issues that impact the simulation of turbulence Provides a range of examples of large eddy simulation techniques Discusses the challenges posed by boundary conditions in turbulence simulation and provides approaches to addressing them

partial differential equations and applications

Giorgio Talenti
partial differential equations and applications Book PDF

Author : Giorgio Talenti
Publisher : Routledge
Page : 276 pages
File Size : 52,9 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781351425834

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partial differential equations and applications by Giorgio Talenti Pdf

Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.

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 : 54,5 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.​

Problems and Methods in Mathematical Physics

Johannes Elschner,Israel Gohberg,Bernd Silbermann
Problems and Methods in Mathematical Physics Book PDF

Author : Johannes Elschner,Israel Gohberg,Bernd Silbermann
Publisher : Birkhäuser
Page : 530 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034882767

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Problems and Methods in Mathematical Physics by Johannes Elschner,Israel Gohberg,Bernd Silbermann Pdf

This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried Prössdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect Prössdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried Prössdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

Electromagnetic Modeling by Finite Element Methods

João Pedro A. Bastos,Nelson Sadowski
Electromagnetic Modeling by Finite Element Methods Book PDF

Author : João Pedro A. Bastos,Nelson Sadowski
Publisher : CRC Press
Page : 512 pages
File Size : 42,8 Mb
Release : 2003-04-01
Category : Technology & Engineering
ISBN : 0203911172

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Electromagnetic Modeling by Finite Element Methods by João Pedro A. Bastos,Nelson Sadowski Pdf

Unlike any other source in the field, this valuable reference clearly examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. The authors examine phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the elect

High-Order Methods for Incompressible Fluid Flow

M. O. Deville,P. F. Fischer,E. H. Mund
High Order Methods for Incompressible Fluid Flow Book PDF

Author : M. O. Deville,P. F. Fischer,E. H. Mund
Publisher : Cambridge University Press
Page : 532 pages
File Size : 40,8 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0521453097

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High-Order Methods for Incompressible Fluid Flow by M. O. Deville,P. F. Fischer,E. H. Mund Pdf

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The Hybrid High-Order Method for Polytopal Meshes

Daniele Antonio Di Pietro,Jérôme Droniou
The Hybrid High Order Method for Polytopal Meshes Book PDF

Author : Daniele Antonio Di Pietro,Jérôme Droniou
Publisher : Springer Nature
Page : 552 pages
File Size : 43,6 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9783030372033

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The Hybrid High-Order Method for Polytopal Meshes by Daniele Antonio Di Pietro,Jérôme Droniou Pdf

This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.