An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method PDF Download
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Author: Shukai Du
Publisher: Springer Nature
ISBN: 3030272303
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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.
Author: Shukai Du
Publisher: Springer Nature
ISBN: 3030272303
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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.
Author: Matteo Cicuttin
Publisher: Springer Nature
ISBN: 3030814777
Category : Mathematics
Languages : en
Pages : 138
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Book Description
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.
Author: Bernardo Cockburn
Publisher:
ISBN:
Category :
Languages : en
Pages : 418
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Book Description
Author: Daniele Antonio Di Pietro
Publisher: Springer
ISBN: 3319946765
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
Author: Gabriel R. Barrenechea
Publisher: Springer
ISBN: 3319416405
Category : Computers
Languages : en
Pages : 433
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Book Description
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: 3642229808
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Houssem Haddar
Publisher: Springer
ISBN: 3319193066
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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.
Author: Erwin Stein
Publisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 870
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Book Description
The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.
Author: Carsten Carstensen
Publisher: Springer Science & Business Media
ISBN: 9783540443926
Category : Computers
Languages : en
Pages : 234
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Book Description
The contributions in this book by leading international experts in the field of electromagnetic field computation cover a wide area of contemporary research activities. They clearly underline the important role of modeling, analysis and numerical methods to provide powerful tools for the simulation of electromagnetic phenomena. The main topics range from the mathematical analysis of Maxwell's equations including its proper spatial discretizations (edge elements, boundary element methods, finite integration), and efficient iterative solution techniques (multigrid, domain decomposition) to multiscale aspects in micromagnetics. The reader will get acquainted with many facets of modern computational techniques and its applications to relevant problems in electromagnetism.
Author: Jochen Blath
Publisher: Cambridge University Press
ISBN: 052171821X
Category : Mathematics
Languages : en
Pages : 397
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Book Description
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.
