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BEM-based Finite Element Approaches on Polytopal Meshes

2019-07-18 Computers
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Release : 2019-07-18
Genre : Computers
Kind : eBook
Book Rating : 61X/5 ( reviews)

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Book Synopsis BEM-based Finite Element Approaches on Polytopal Meshes by : Steffen Weißer

Download or read book BEM-based Finite Element Approaches on Polytopal Meshes written by Steffen Weißer. This book was released on 2019-07-18. Available in PDF, EPUB and Kindle. Book excerpt: 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

2020-10-30 Mathematics
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Release : 2020-10-30
Genre : Mathematics
Kind : eBook
Book Rating : 699/5 ( reviews)

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

Download or read book An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases written by Francis X. Giraldo. This book was released on 2020-10-30. Available in PDF, EPUB and Kindle. Book excerpt: 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

2019-09-26 Mathematics
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Release : 2019-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen

Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen. This book was released on 2019-09-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018

2020-08-11 Mathematics
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Release : 2020-08-11
Genre : Mathematics
Kind : eBook
Book Rating : 006/5 ( reviews)

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Book Synopsis Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 by : Gabriel R. Barrenechea

Download or read book Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 written by Gabriel R. Barrenechea. This book was released on 2020-08-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Geometry, Grid Generation and Scientific Computing

2021-09-25 Mathematics
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Release : 2021-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 981/5 ( reviews)

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Book Synopsis Numerical Geometry, Grid Generation and Scientific Computing by : Vladimir A. Garanzha

Download or read book Numerical Geometry, Grid Generation and Scientific Computing written by Vladimir A. Garanzha. This book was released on 2021-09-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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