Hybrid High Order Methods

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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 : 45,5 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.

The Hybrid High-Order Method for Polytopal Meshes

Daniele Antonio Di Pietro,Jérôme Droniou
The Hybrid High Order Method for Polytopal Meshes Book PDF

Author : Daniele Antonio Di Pietro,Jérôme Droniou
Publisher : Springer Nature
Page : 552 pages
File Size : 42,9 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9783030372033

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The Hybrid High-Order Method for Polytopal Meshes by Daniele Antonio Di Pietro,Jérôme Droniou Pdf

This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.

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 : 49,6 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.

Adaptive High-order Methods in Computational Fluid Dynamics

Z. J. Wang
Adaptive High order Methods in Computational Fluid Dynamics Book PDF

Author : Z. J. Wang
Publisher : World Scientific
Page : 471 pages
File Size : 44,8 Mb
Release : 2011
Category : Science
ISBN : 9789814313186

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Adaptive High-order Methods in Computational Fluid Dynamics by Z. J. Wang Pdf

This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

High-Order Methods for Incompressible Fluid Flow

M. O. Deville,P. F. Fischer,E. H. Mund
High Order Methods for Incompressible Fluid Flow Book PDF

Author : M. O. Deville,P. F. Fischer,E. H. Mund
Publisher : Cambridge University Press
Page : 532 pages
File Size : 45,7 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0521453097

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High-Order Methods for Incompressible Fluid Flow by M. O. Deville,P. F. Fischer,E. H. Mund Pdf

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High Order Difference Methods for Time Dependent PDE

Bertil Gustafsson
High Order Difference Methods for Time Dependent PDE Book PDF

Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 43,6 Mb
Release : 2007-12-06
Category : Mathematics
ISBN : 9783540749936

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High Order Difference Methods for Time Dependent PDE by Bertil Gustafsson Pdf

This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020 1 Book PDF

Author : Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab
Publisher : Springer Nature
Page : 571 pages
File Size : 41,6 Mb
Release : 2023-06-30
Category : Mathematics
ISBN : 9783031204326

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab Pdf

The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.

Finite Elements II

Alexandre Ern,Jean-Luc Guermond
Finite Elements II Book PDF

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Nature
Page : 491 pages
File Size : 52,8 Mb
Release : 2021-04-22
Category : Mathematics
ISBN : 9783030569235

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Finite Elements II by Alexandre Ern,Jean-Luc Guermond Pdf

This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Robert Klöfkorn,Eirik Keilegavlen,Florin A. Radu,Jürgen Fuhrmann
Finite Volumes for Complex Applications IX Methods Theoretical Aspects Examples Book PDF

Author : Robert Klöfkorn,Eirik Keilegavlen,Florin A. Radu,Jürgen Fuhrmann
Publisher : Springer Nature
Page : 727 pages
File Size : 47,8 Mb
Release : 2020-06-09
Category : Computers
ISBN : 9783030436513

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Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples by Robert Klöfkorn,Eirik Keilegavlen,Florin A. Radu,Jürgen Fuhrmann Pdf

The proceedings of the 9th conference on "Finite Volumes for Complex Applications" (Bergen, June 2020) are structured in two volumes. The first volume collects the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Topics covered include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. Altogether, a rather comprehensive overview is given on the state of the art in the field. The properties of the methods considered in the conference give them distinguished advantages for a number of applications. These include fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory, carbon capture utilization and storage, geothermal energy and further topics. The second volume covers reviewed contributions reporting successful applications of finite volume and related methods in these fields. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability, making the finite volume methods compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

Numerical Mathematics and Advanced Applications ENUMATH 2017

Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Numerical Mathematics and Advanced Applications ENUMATH 2017 Book PDF

Author : Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Publisher : Springer
Page : 1070 pages
File Size : 47,9 Mb
Release : 2019-01-05
Category : Computers
ISBN : 9783319964157

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Numerical Mathematics and Advanced Applications ENUMATH 2017 by Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop Pdf

This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, 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. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).

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 : 55,5 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.

Polyhedral Methods in Geosciences

Daniele Antonio Di Pietro,Luca Formaggia,Roland Masson
Polyhedral Methods in Geosciences Book PDF

Author : Daniele Antonio Di Pietro,Luca Formaggia,Roland Masson
Publisher : Springer Nature
Page : 342 pages
File Size : 53,8 Mb
Release : 2021-06-14
Category : Mathematics
ISBN : 9783030693633

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Polyhedral Methods in Geosciences by Daniele Antonio Di Pietro,Luca Formaggia,Roland Masson Pdf

The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge of advanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.

Spectral and High Order Methods for Partial Differential Equations

Jan S. Hesthaven,Einar M. Rønquist
Spectral and High Order Methods for Partial Differential Equations Book PDF

Author : Jan S. Hesthaven,Einar M. Rønquist
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 47,9 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9783642153372

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Spectral and High Order Methods for Partial Differential Equations by Jan S. Hesthaven,Einar M. Rønquist Pdf

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach

Norbert Kroll,Charles Hirsch,Francesco Bassi,Craig Johnston,Koen Hillewaert
IDIHOM Industrialization of High Order Methods A Top Down Approach Book PDF

Author : Norbert Kroll,Charles Hirsch,Francesco Bassi,Craig Johnston,Koen Hillewaert
Publisher : Springer
Page : 686 pages
File Size : 53,6 Mb
Release : 2015-01-02
Category : Technology & Engineering
ISBN : 9783319128863

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IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach by Norbert Kroll,Charles Hirsch,Francesco Bassi,Craig Johnston,Koen Hillewaert Pdf

The book describes the main findings of the EU-funded project IDIHOM (Industrialization of High-Order Methods – A Top-Down Approach). The goal of this project was the improvement, utilization and demonstration of innovative higher-order simulation capabilities for large-scale aerodynamic application challenges in the aircraft industry. The IDIHOM consortium consisted of 21 organizations, including aircraft manufacturers, software vendors, as well as the major European research establishments and several universities, all of them with proven expertise in the field of computational fluid dynamics. After a general introduction to the project, the book reports on new approaches for curved boundary-grid generation, high-order solution methods and visualization techniques. It summarizes the achievements, weaknesses and perspectives of the new simulation capabilities developed by the project partners for various industrial applications, and includes internal- and external-aerodynamic as well as multidisciplinary test cases.

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
Page : 658 pages
File Size : 50,8 Mb
Release : 2020-09-11
Category : Mathematics
ISBN : 3030396495

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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.