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Computational Framework for the Finite Element Method in MATLAB and Python

Author: Pavel Sumets

Publisher:

Published: 2022

Total Pages:

ISBN-13: 9781032209272

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"Computational Framework for the Finite Element Method in MATLAB and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM. Suitable for upper-level undergraduates and graduates in applied mathematics, science, or engineering. Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation"--

Book Synopsis Computational Framework for the Finite Element Method in MATLAB and Python by : Pavel Sumets

Download or read book Computational Framework for the Finite Element Method in MATLAB and Python written by Pavel Sumets and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Computational Framework for the Finite Element Method in MATLAB and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM. Suitable for upper-level undergraduates and graduates in applied mathematics, science, or engineering. Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation"--

Computational Framework for the Finite Element Method in MATLAB® and Python

Author: Pavel Sumets

Publisher: CRC Press

Published: 2022-08-11

Total Pages: 166

ISBN-13: 1000610020

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Computational Framework for the Finite Element Method in MATLAB® and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB® language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM Suitable for upper-level undergraduates and graduates in applied mathematics, science or engineering Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation

Book Synopsis Computational Framework for the Finite Element Method in MATLAB® and Python by : Pavel Sumets

Download or read book Computational Framework for the Finite Element Method in MATLAB® and Python written by Pavel Sumets and published by CRC Press. This book was released on 2022-08-11 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Framework for the Finite Element Method in MATLAB® and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB® language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM Suitable for upper-level undergraduates and graduates in applied mathematics, science or engineering Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation

MATLAB and C Programming for Trefftz Finite Element Methods

Author: Qing-Hua Qin

Publisher: CRC Press

Published: 2008-07-21

Total Pages: 464

ISBN-13: 1420072765

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Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in t

Book Synopsis MATLAB and C Programming for Trefftz Finite Element Methods by : Qing-Hua Qin

Download or read book MATLAB and C Programming for Trefftz Finite Element Methods written by Qing-Hua Qin and published by CRC Press. This book was released on 2008-07-21 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in t

The Finite Element Method Using MATLAB

Author: Young W. Kwon

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 624

ISBN-13: 1420041886

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Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis. What's new in the Second Edition? Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

Book Synopsis The Finite Element Method Using MATLAB by : Young W. Kwon

Download or read book The Finite Element Method Using MATLAB written by Young W. Kwon and published by CRC Press. This book was released on 2018-10-03 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis. What's new in the Second Edition? Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

MATLAB Codes for Finite Element Analysis

Author: Antonio J. M. Ferreira

Publisher: Springer Nature

Published: 2020-06-16

Total Pages: 354

ISBN-13: 3030479528

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This book illustrates how MATLAB compact and powerful programming framework can be very useful in the finite element analysis of solids and structures. The book shortly introduces finite element concepts and an extensive list of MATLAB codes for readers to use and modify. The book areas range from very simple springs and bars to more complex beams and plates in static bending, free vibrations, buckling and time transient problems. Moreover, laminated and functionally graded material structures are introduced and solved.

Book Synopsis MATLAB Codes for Finite Element Analysis by : Antonio J. M. Ferreira

Download or read book MATLAB Codes for Finite Element Analysis written by Antonio J. M. Ferreira and published by Springer Nature. This book was released on 2020-06-16 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates how MATLAB compact and powerful programming framework can be very useful in the finite element analysis of solids and structures. The book shortly introduces finite element concepts and an extensive list of MATLAB codes for readers to use and modify. The book areas range from very simple springs and bars to more complex beams and plates in static bending, free vibrations, buckling and time transient problems. Moreover, laminated and functionally graded material structures are introduced and solved.

Automated Solution of Differential Equations by the Finite Element Method

Author: Anders Logg

Publisher: Springer Science & Business Media

Published: 2012-02-24

Total Pages: 723

ISBN-13: 3642230997

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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.

Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

MATLAB Guide to Finite Elements

Author: Peter I. Kattan

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 392

ISBN-13: 3662052091

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This book explores numerical implementation of Finite Element Analysis using MATLAB. Stressing interactive use of MATLAB, it provides examples and exercises from mechanical, civil and aerospace engineering as well as materials science. The text includes a short MATLAB tutorial. An extensive solutions manual offers detailed solutions to all problems in the book for classroom use. The second edition includes a new brick (solid) element with eight nodes and a one-dimensional fluid flow element. Also added is a review of applications of finite elements in fluid flow, heat transfer, structural dynamics and electro-magnetics. The accompanying CD-ROM presents more than fifty MATLAB functions.

Book Synopsis MATLAB Guide to Finite Elements by : Peter I. Kattan

Download or read book MATLAB Guide to Finite Elements written by Peter I. Kattan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores numerical implementation of Finite Element Analysis using MATLAB. Stressing interactive use of MATLAB, it provides examples and exercises from mechanical, civil and aerospace engineering as well as materials science. The text includes a short MATLAB tutorial. An extensive solutions manual offers detailed solutions to all problems in the book for classroom use. The second edition includes a new brick (solid) element with eight nodes and a one-dimensional fluid flow element. Also added is a review of applications of finite elements in fluid flow, heat transfer, structural dynamics and electro-magnetics. The accompanying CD-ROM presents more than fifty MATLAB functions.

Development and Application of the Finite Element Method based on MatLab

Author: Herbert Baaser

Publisher: Springer Science & Business Media

Published: 2010-05-10

Total Pages: 70

ISBN-13: 3642131530

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The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer–oriented mechanics, so that many scienti?c brancheshavegrownup besides overthelastdecades. Nevertheless,theFEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for e?ective pre– and postprocessors are available in the meantime. Due to that, today it is a quite challenging task to operate with all these di?erent tools at the same time and to understand all handling and so- tion techniques developed over the last years. So, we want to help in getting a deeper insight into the main “interfaces” between the “customers of the FEM” and the codes itself by providing a totally open structured FE–code based on Matlab, which is a very powerful tool in operating with matrix based formulations. That idea and conditions forced us some years ago to initiateDAEdalon as a tool for general FE developments in research appli- tions. In spite of still existing high sophisticated – mostly commercial – FE codes, the success and the acceptance of such a structured tool justify that decision afterwards more and more.

Book Synopsis Development and Application of the Finite Element Method based on MatLab by : Herbert Baaser

Download or read book Development and Application of the Finite Element Method based on MatLab written by Herbert Baaser and published by Springer Science & Business Media. This book was released on 2010-05-10 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer–oriented mechanics, so that many scienti?c brancheshavegrownup besides overthelastdecades. Nevertheless,theFEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for e?ective pre– and postprocessors are available in the meantime. Due to that, today it is a quite challenging task to operate with all these di?erent tools at the same time and to understand all handling and so- tion techniques developed over the last years. So, we want to help in getting a deeper insight into the main “interfaces” between the “customers of the FEM” and the codes itself by providing a totally open structured FE–code based on Matlab, which is a very powerful tool in operating with matrix based formulations. That idea and conditions forced us some years ago to initiateDAEdalon as a tool for general FE developments in research appli- tions. In spite of still existing high sophisticated – mostly commercial – FE codes, the success and the acceptance of such a structured tool justify that decision afterwards more and more.

The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson

Publisher: Springer Science & Business Media

Published: 2013-01-13

Total Pages: 403

ISBN-13: 3642332870

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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.

Book Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson

Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Understanding and Implementing the Finite Element Method

Author: Mark S. Gockenbach

Publisher: SIAM

Published: 2006-01-01

Total Pages: 363

ISBN-13: 0898717841

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Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.

Book Synopsis Understanding and Implementing the Finite Element Method by : Mark S. Gockenbach

Download or read book Understanding and Implementing the Finite Element Method written by Mark S. Gockenbach and published by SIAM. This book was released on 2006-01-01 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.