Geometrically Unfitted Finite Element Methods And Applications

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Geometrically Unfitted Finite Element Methods and Applications

Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Geometrically Unfitted Finite Element Methods and Applications Book PDF

Author : Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Publisher : Springer
Page : 361 pages
File Size : 44,9 Mb
Release : 2018-03-13
Category : Mathematics
ISBN : 9783319714318

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Geometrically Unfitted Finite Element Methods and Applications by Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii Pdf

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.

Advanced Finite Element Methods with Applications

Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Advanced Finite Element Methods with Applications Book PDF

Author : Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publisher : Springer
Page : 428 pages
File Size : 55,7 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030142445

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Advanced Finite Element Methods with Applications by Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach Pdf

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Geometric Partial Differential Equations - Part I

Anonim
Geometric Partial Differential Equations Part I Book PDF

Author : Anonim
Publisher : Elsevier
Page : 710 pages
File Size : 50,6 Mb
Release : 2020-01-14
Category : Mathematics
ISBN : 9780444640048

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Geometric Partial Differential Equations - Part I by Anonim Pdf

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018

Gabriel R. Barrenechea,John Mackenzie
Boundary and Interior Layers Computational and Asymptotic Methods BAIL 2018 Book PDF

Author : Gabriel R. Barrenechea,John Mackenzie
Publisher : Springer Nature
Page : 254 pages
File Size : 52,8 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9783030418007

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Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 by Gabriel R. Barrenechea,John Mackenzie Pdf

This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.

Partition of Unity Methods

Stéphane P. A. Bordas,Alexander Menk,Sundararajan Natarajan
Partition of Unity Methods Book PDF

Author : Stéphane P. A. Bordas,Alexander Menk,Sundararajan Natarajan
Publisher : John Wiley & Sons
Page : 373 pages
File Size : 51,6 Mb
Release : 2023-10-19
Category : Technology & Engineering
ISBN : 9781118535882

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Partition of Unity Methods by Stéphane P. A. Bordas,Alexander Menk,Sundararajan Natarajan Pdf

PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.

Numerical Geometry, Grid Generation and Scientific Computing

Vladimir A. Garanzha,Lennard Kamenski,Hang Si
Numerical Geometry Grid Generation and Scientific Computing Book PDF

Author : Vladimir A. Garanzha,Lennard Kamenski,Hang Si
Publisher : Springer Nature
Page : 419 pages
File Size : 54,6 Mb
Release : 2021-09-25
Category : Mathematics
ISBN : 9783030767983

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Numerical Geometry, Grid Generation and Scientific Computing by Vladimir A. Garanzha,Lennard Kamenski,Hang Si Pdf

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

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 : 47,8 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.

Isogeometric Analysis and Applications 2018

Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler
Isogeometric Analysis and Applications 2018 Book PDF

Author : Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler
Publisher : Springer Nature
Page : 279 pages
File Size : 53,9 Mb
Release : 2021-01-13
Category : Mathematics
ISBN : 9783030498368

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Isogeometric Analysis and Applications 2018 by Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler Pdf

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018. This conference series, previously held in Linz, Austria, in 2012 and Annweiler am Trifels, Germany, in 2014, has created an international forum for interaction between scientists and practitioners working in this rapidly developing field. Isogeometric analysis is a groundbreaking computational approach that aims to bridge the gap between numerical analysis and computational geometry modeling by integrating the finite element method and related numerical simulation techniques into the computer-aided design workflow, and vice versa. The methodology has matured over the last decade both in terms of our theoretical understanding, its mathematical foundation and the robustness and efficiency of its practical implementations. This development has enabled scientists and practitioners to tackle challenging new applications at the frontiers of research in science and engineering and attracted early adopters for this his novel computer-aided design and engineering technology in industry. The IGAA 2018 conference brought together experts on isogeometric analysis theory and application, share their insights into challenging industrial applications and to discuss the latest developments as well as the directions of future research and development that are required to make isogeometric analysis an established mainstream technology.

BEM-based Finite Element Approaches on Polytopal Meshes

Steffen Weißer
BEM based Finite Element Approaches on Polytopal Meshes Book PDF

Author : Steffen Weißer
Publisher : Springer
Page : 246 pages
File Size : 52,6 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9783030209612

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BEM-based Finite Element Approaches on Polytopal Meshes by Steffen Weißer Pdf

This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.

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 : 48,5 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.

Finite Elements for Analysis and Design

J. E. Akin
Finite Elements for Analysis and Design Book PDF

Author : J. E. Akin
Publisher : Elsevier
Page : 563 pages
File Size : 52,9 Mb
Release : 2014-06-28
Category : Technology & Engineering
ISBN : 9780080506470

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Finite Elements for Analysis and Design by J. E. Akin Pdf

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material. Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing Basic theory has been added in the book, including worked examples to enable students to understand the concepts Contains coverage of computational topics, including worked examples to enable students to understand concepts Improved coverage of sensitivity analysis and computational fluid dynamics Uses example applications to increase students' understanding Includes a disk with the FORTRAN source for the programs cided in the text

Computational Methods for Fracture

Timon Rabczuk
Computational Methods for Fracture Book PDF

Author : Timon Rabczuk
Publisher : MDPI
Page : 406 pages
File Size : 54,5 Mb
Release : 2019-10-28
Category : Technology & Engineering
ISBN : 9783039216864

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Computational Methods for Fracture by Timon Rabczuk Pdf

This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.

Exercises in Numerical Linear Algebra and Matrix Factorizations

Tom Lyche,Georg Muntingh,Øyvind Ryan
Exercises in Numerical Linear Algebra and Matrix Factorizations Book PDF

Author : Tom Lyche,Georg Muntingh,Øyvind Ryan
Publisher : Springer Nature
Page : 265 pages
File Size : 46,9 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9783030597894

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Exercises in Numerical Linear Algebra and Matrix Factorizations by Tom Lyche,Georg Muntingh,Øyvind Ryan Pdf

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.

IGA

Robin Bouclier,Thibaut Hirschler
IGA Book PDF

Author : Robin Bouclier,Thibaut Hirschler
Publisher : John Wiley & Sons
Page : 260 pages
File Size : 48,6 Mb
Release : 2022-06-06
Category : Mathematics
ISBN : 9781119988540

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IGA by Robin Bouclier,Thibaut Hirschler Pdf

Isogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, about fifteen years after its creation, substantial works are being reported in IGA, which make it very competitive in scientific computing. This book provides a contemporary vision of IGA by first discussing the current challenges in achieving a true bridge between design and analysis, then proposing original solutions that answer the issues from an analytical point of view, and, eventually, studying the shape optimization of structures, which is one of the greatest applications of IGA. To handle complex structures, a full analysis-to-optimization framework is developed, based on non-invasive coupling, parallel domain decomposition and immersed geometrical modeling. This seems to be very robust, taking on all of the attractive features of IGA (the design–analysis link, numerical efficiency and natural regularization), giving us the opportunity to explore new types of design.

Numerical Mathematics and Advanced Applications ENUMATH 2019

Fred J. Vermolen,Cornelis Vuik
Numerical Mathematics and Advanced Applications ENUMATH 2019 Book PDF

Author : Fred J. Vermolen,Cornelis Vuik
Publisher : Springer Nature
Page : 1185 pages
File Size : 46,6 Mb
Release : 2021-04-30
Category : Mathematics
ISBN : 9783030558741

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Numerical Mathematics and Advanced Applications ENUMATH 2019 by Fred J. Vermolen,Cornelis Vuik Pdf

This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).