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An Invitation To The Theory Of The Hybridizable Discontinuous Galerkin Method
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Book Synopsis An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method by : Shukai Du
Download or read book An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method written by Shukai Du and published by Springer Nature. This book was released on 2019-08-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
Book Synopsis Hybrid High-Order Methods by : Matteo Cicuttin
Download or read book Hybrid High-Order Methods written by Matteo Cicuttin and published by Springer Nature. This book was released on 2021-11-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hybridizable Discontinuous Galerkin Method for Curved Domains by : Manuel Esteban Solano Palma
Download or read book Hybridizable Discontinuous Galerkin Method for Curved Domains written by Manuel Esteban Solano Palma and published by . This book was released on 2012 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 and published by Springer Nature. This book was released on 2020-10-30 with total page 559 pages. 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.
Book Synopsis Generalized Projection-based Error Analysis of Hybridizable Discontinuous Galerkin Methods by : Shukai Du
Download or read book Generalized Projection-based Error Analysis of Hybridizable Discontinuous Galerkin Methods written by Shukai Du and published by . This book was released on 2020 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: For some hybridizable discontinuous Galerkin (HDG) methods, suitably devised projections make their analyses simple and concise. However, devising these projections is usually difficult and many important HDG methods still lack their corresponding projections; consequently, their analyses become cumbersome. In this thesis, we propose novel analytical tools to solve this problem. These tools can be used to systematically devise and analyze new HDG methods, to unify their analyses, and to simplify and improve existing ones. We shall study these tools and their applications in three cases: (1) HDG methods for elastic problems, (2) HDG methods on polyhedral meshes, and (3) HDG methods for Maxwell equations. They will be discussed in Chapter 2, Chapter 3, and Chapter 4, respectively. In Chapter 1, we give an introduction to motivate the topic of this thesis. Finally in Chapter 5, we conclude by discussing several promising potential developments of our work.
Book Synopsis Implementation of an Implicit-explicit Scheme for Hybridizable Discontinuous Galerkin by : Lauren Nicole Kolkman
Download or read book Implementation of an Implicit-explicit Scheme for Hybridizable Discontinuous Galerkin written by Lauren Nicole Kolkman and published by . This book was released on 2018 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods, specifically Hybridizable Discontinuous Galerkin (HDG), are used in many applications. One choice made when implementing HDG for a specific problem is whether time integration should be performed implicitly or explicitly. Both approaches have their advantages but, for some problems, a combination of these methods is a better choice than either on their own. Thus, an implicit-explicit (IMEX) scheme that splits the computational domain into implicit and explicit regions based on the domain geometry is considered in this thesis. This allows for stability throughout the domain and exploits the advantages each scheme has to offer. A study of the convergence and properties of this implementation of the IMEX method is presented along with comparisons to the individual methods.
Book Synopsis Numerical Methods for PDEs by : Daniele Antonio Di Pietro
Download or read book Numerical Methods for PDEs written by Daniele Antonio Di Pietro and published by Springer. This book was released on 2018-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations by : Gabriel R. Barrenechea
Download or read book Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations written by Gabriel R. Barrenechea and published by Springer. This book was released on 2016-10-03 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Daniele Antonio Di Pietro Publisher :Springer Science & Business Media ISBN 13 :3642229808 Total Pages :392 pages Book Rating :4.6/5 (422 download)
Book Synopsis Mathematical Aspects of Discontinuous Galerkin Methods by : Daniele Antonio Di Pietro
Download or read book Mathematical Aspects of Discontinuous Galerkin Methods written by Daniele Antonio Di Pietro and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.
Book Synopsis Computational Electromagnetism by : Houssem Haddar
Download or read book Computational Electromagnetism written by Houssem Haddar and published by Springer. This book was released on 2015-07-20 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.
Book Synopsis An Introduction to Computational Stochastic PDEs by : Gabriel J. Lord
Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Book Synopsis Computational Methods in Applied Sciences by : Ch Hirsch
Download or read book Computational Methods in Applied Sciences written by Ch Hirsch and published by Elsevier Publishing Company. This book was released on 1992 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Computational Fluid Dynamics Conference and the European Conference on Numerical Methods in Engineering are the initiative of national Scientific Societies of many countries in Europe engaged in these fields. The 28 papers in this volume give an extensive review on selected topics pertaining to basic methodologies, scientific developments and industrial applications, in fluid dynamics, in structural mechanics and other engineering applications. This multidisciplinary volume brings together specialists in a wide range of engineering activities who employ common analytical and experimental methods in their research. The contents are of world-wide interest and will help to stimulate future research and analysis in this broad field.
Book Synopsis The Courant–Friedrichs–Lewy (CFL) Condition by : Carlos A. de Moura
Download or read book The Courant–Friedrichs–Lewy (CFL) Condition written by Carlos A. de Moura and published by Springer Science & Business Media. This book was released on 2012-10-28 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition. A major result in the field of numerical analysis, the CFL condition has influenced the research of many important mathematicians over the past eight decades, and this work is meant to take stock of its most important and current applications. The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years After its Discovery will be of interest to practicing mathematicians, engineers, physicists, and graduate students who work with numerical methods.
Book Synopsis Panther vs Sherman by : Steven J. Zaloga
Download or read book Panther vs Sherman written by Steven J. Zaloga and published by Bloomsbury Publishing. This book was released on 2011-03-15 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Steven J Zaloga offers a fascinating comparison between the two most important tanks involved in the crucial fighting of 1944, the American Sherman and the German Panther. Placing the reader in the heart of this battle between quality and quantity Zaloga uses a compelling account of the ferocious fighting during the Battle of the Bulge to explain the successes and failures of each tank, highlighting the fact that a tank can only be as good as its crew, weighing up the impact of low morale, high cost and mediocre crew training on the Panther's superiority. With full-colour battlescenes, technical drawings, photographs, digital gunsight views, extracts from crew training manuals and real combat reports, this book brings the titanic battles between the Panther and Sherman to life.
Book Synopsis The Coinage of Aksum by : Stuart C. Munro-Hay
Download or read book The Coinage of Aksum written by Stuart C. Munro-Hay and published by . This book was released on 1984 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Trends in Stochastic Analysis by : Jochen Blath
Download or read book Trends in Stochastic Analysis written by Jochen Blath and published by Cambridge University Press. This book was released on 2009-04-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.
Book Synopsis Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other by : Ulrich Daepp
Download or read book Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other written by Ulrich Daepp and published by American Mathematical Soc.. This book was released on 2018 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.
