Hp Version Discontinuous Galerkin Methods On Polygonal And Polyhedral Meshes

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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

Andrea Cangiani,Zhaonan Dong,Emmanuil H. Georgoulis,Paul Houston
hp Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes Book PDF

Author : Andrea Cangiani,Zhaonan Dong,Emmanuil H. Georgoulis,Paul Houston
Publisher : Springer
Page : 131 pages
File Size : 54,6 Mb
Release : 2017-11-27
Category : Mathematics
ISBN : 9783319676739

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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes by Andrea Cangiani,Zhaonan Dong,Emmanuil H. Georgoulis,Paul Houston Pdf

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.

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 : 51,9 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.

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 : 54,7 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.

Advances in Discretization Methods

Giulio Ventura,Elena Benvenuti
Advances in Discretization Methods Book PDF

Author : Giulio Ventura,Elena Benvenuti
Publisher : Springer
Page : 269 pages
File Size : 51,6 Mb
Release : 2016-08-24
Category : Technology & Engineering
ISBN : 9783319412467

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Advances in Discretization Methods by Giulio Ventura,Elena Benvenuti Pdf

This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.

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 : 47,5 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.

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 : 44,5 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.

Mesh Generation and Adaptation

Rubén Sevilla,Simona Perotto,Kenneth Morgan
Mesh Generation and Adaptation Book PDF

Author : Rubén Sevilla,Simona Perotto,Kenneth Morgan
Publisher : Springer Nature
Page : 328 pages
File Size : 46,6 Mb
Release : 2022-05-18
Category : Mathematics
ISBN : 9783030925406

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Mesh Generation and Adaptation by Rubén Sevilla,Simona Perotto,Kenneth Morgan Pdf

The developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.

Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

Kai Hormann,N. Sukumar
Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics Book PDF

Author : Kai Hormann,N. Sukumar
Publisher : CRC Press
Page : 351 pages
File Size : 48,9 Mb
Release : 2017-10-30
Category : Computers
ISBN : 9781498763615

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Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics by Kai Hormann,N. Sukumar Pdf

In Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, eminent computer graphics and computational mechanics researchers provide a state-of-the-art overview of generalized barycentric coordinates. Commonly used in cutting-edge applications such as mesh parametrization, image warping, mesh deformation, and finite as well as boundary element methods, the theory of barycentric coordinates is also fundamental for use in animation and in simulating the deformation of solid continua. Generalized Barycentric Coordinates is divided into three sections, with five chapters each, covering the theoretical background, as well as their use in computer graphics and computational mechanics. A vivid 16-page insert helps illustrating the stunning applications of this fascinating research area. Key Features: Provides an overview of the many different types of barycentric coordinates and their properties. Discusses diverse applications of barycentric coordinates in computer graphics and computational mechanics. The first book-length treatment on this topic

75 Years of Mathematics of Computation

Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
75 Years of Mathematics of Computation Book PDF

Author : Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 51,8 Mb
Release : 2020-07-29
Category : Education
ISBN : 9781470451639

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75 Years of Mathematics of Computation by Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld Pdf

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

Parallel and Distributed Computing, Applications and Technologies

Hong Shen,Yingpeng Sang,Yong Zhang,Nong Xiao,Hamid R. Arabnia,Geoffrey Fox,Ajay Gupta,Manu Malek
Parallel and Distributed Computing Applications and Technologies Book PDF

Author : Hong Shen,Yingpeng Sang,Yong Zhang,Nong Xiao,Hamid R. Arabnia,Geoffrey Fox,Ajay Gupta,Manu Malek
Publisher : Springer Nature
Page : 643 pages
File Size : 45,9 Mb
Release : 2022-03-15
Category : Computers
ISBN : 9783030967727

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Parallel and Distributed Computing, Applications and Technologies by Hong Shen,Yingpeng Sang,Yong Zhang,Nong Xiao,Hamid R. Arabnia,Geoffrey Fox,Ajay Gupta,Manu Malek Pdf

This book constitutes the proceedings of the 22nd International Conference on Parallel and Distributed Computing, Applications, and Technologies, PDCAT 2021, which took place in Guangzhou, China, during December 17-19, 2021. The 24 full papers and 34 short papers included in this volume were carefully reviewed and selected from 97 submissions. The papers are categorized into the following topical sub-headings: networking and architectures, software systems and technologies, algorithms and applications, and security and privacy.

Anisotropic hp-Mesh Adaptation Methods

Vít Dolejší,Georg May
Anisotropic hp Mesh Adaptation Methods Book PDF

Author : Vít Dolejší,Georg May
Publisher : Springer Nature
Page : 258 pages
File Size : 48,6 Mb
Release : 2022-06-06
Category : Mathematics
ISBN : 9783031042799

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Anisotropic hp-Mesh Adaptation Methods by Vít Dolejší,Georg May Pdf

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Mejdi Azaïez,Henda El Fekih,Jan S. Hesthaven
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 Book PDF

Author : Mejdi Azaïez,Henda El Fekih,Jan S. Hesthaven
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 50,7 Mb
Release : 2013-11-19
Category : Mathematics
ISBN : 9783319016016

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Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 by Mejdi Azaïez,Henda El Fekih,Jan S. Hesthaven 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 (2012), and provides an overview of the depth and breath 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. ​

Approximation Theory XV: San Antonio 2016

Gregory E. Fasshauer,Larry L. Schumaker
Approximation Theory XV San Antonio 2016 Book PDF

Author : Gregory E. Fasshauer,Larry L. Schumaker
Publisher : Springer
Page : 398 pages
File Size : 46,8 Mb
Release : 2017-07-19
Category : Mathematics
ISBN : 9783319599120

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Approximation Theory XV: San Antonio 2016 by Gregory E. Fasshauer,Larry L. Schumaker Pdf

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.

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 : 52,6 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.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

Robert M. Kirby,Martin Berzins,Jan S. Hesthaven
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 Book PDF

Author : Robert M. Kirby,Martin Berzins,Jan S. Hesthaven
Publisher : Springer
Page : 530 pages
File Size : 51,8 Mb
Release : 2015-11-26
Category : Computers
ISBN : 9783319198002

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 by Robert M. Kirby,Martin Berzins,Jan S. Hesthaven 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 (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.