Building Bridges Connections And Challenges In Modern Approaches To Numerical Partial Differential Equations

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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Gabriel R. Barrenechea,Franco Brezzi,Andrea Cangiani,Emmanuil H. Georgoulis
Building Bridges Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations Book PDF

Author : Gabriel R. Barrenechea,Franco Brezzi,Andrea Cangiani,Emmanuil H. Georgoulis
Publisher : Springer
Page : 433 pages
File Size : 50,6 Mb
Release : 2016-10-03
Category : Computers
ISBN : 9783319416403

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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations by Gabriel R. Barrenechea,Franco Brezzi,Andrea Cangiani,Emmanuil H. Georgoulis Pdf

This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

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 : 53,5 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.

Meshfree Methods for Partial Differential Equations IX

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations IX Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer
Page : 206 pages
File Size : 46,6 Mb
Release : 2019-06-19
Category : Mathematics
ISBN : 9783030151195

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Meshfree Methods for Partial Differential Equations IX by Michael Griebel,Marc Alexander Schweitzer Pdf

This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the 2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.

Meshfree Methods for Partial Differential Equations VIII

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations VIII Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer
Page : 240 pages
File Size : 47,8 Mb
Release : 2017-04-05
Category : Computers
ISBN : 9783319519548

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Meshfree Methods for Partial Differential Equations VIII by Michael Griebel,Marc Alexander Schweitzer Pdf

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 Book PDF

Author : Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Publisher : Springer Nature
Page : 658 pages
File Size : 52,7 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9783030396473

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 by Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab Pdf

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Marco L. Bittencourt,Ney A. Dumont,Jan S. Hesthaven
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 Book PDF

Author : Marco L. Bittencourt,Ney A. Dumont,Jan S. Hesthaven
Publisher : Springer
Page : 700 pages
File Size : 52,9 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783319658704

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 by Marco L. Bittencourt,Ney A. Dumont,Jan S. Hesthaven Pdf

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

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 : 42,5 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.

Numerical Methods for Flows

Harald van Brummelen,Alessandro Corsini,Simona Perotto,Gianluigi Rozza
Numerical Methods for Flows Book PDF

Author : Harald van Brummelen,Alessandro Corsini,Simona Perotto,Gianluigi Rozza
Publisher : Springer Nature
Page : 358 pages
File Size : 49,5 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030307059

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Numerical Methods for Flows by Harald van Brummelen,Alessandro Corsini,Simona Perotto,Gianluigi Rozza Pdf

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

Hybrid High-Order Methods

Matteo Cicuttin,Alexandre Ern,Nicolas Pignet
Hybrid High Order Methods Book PDF

Author : Matteo Cicuttin,Alexandre Ern,Nicolas Pignet
Publisher : Springer Nature
Page : 138 pages
File Size : 41,9 Mb
Release : 2021-11-11
Category : Mathematics
ISBN : 9783030814779

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Hybrid High-Order Methods by Matteo Cicuttin,Alexandre Ern,Nicolas Pignet Pdf

This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.

Numerical Methods for PDEs

Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Numerical Methods for PDEs Book PDF

Author : Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Publisher : Springer
Page : 312 pages
File Size : 44,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319946764

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Numerical Methods for PDEs by Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia Pdf

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

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 : 49,8 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).

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 : 46,8 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.

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 : 45,8 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.

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 : 53,7 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.

Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing

Tetsuya Sakurai,Shao-Liang Zhang,Toshiyuki Imamura,Yusaku Yamamoto,Yoshinobu Kuramashi,Takeo Hoshi
Eigenvalue Problems Algorithms Software and Applications in Petascale Computing Book PDF

Author : Tetsuya Sakurai,Shao-Liang Zhang,Toshiyuki Imamura,Yusaku Yamamoto,Yoshinobu Kuramashi,Takeo Hoshi
Publisher : Springer
Page : 313 pages
File Size : 50,8 Mb
Release : 2018-01-03
Category : Computers
ISBN : 9783319624266

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Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing by Tetsuya Sakurai,Shao-Liang Zhang,Toshiyuki Imamura,Yusaku Yamamoto,Yoshinobu Kuramashi,Takeo Hoshi Pdf

This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.