Hp Version Discontinuous Galerkin Methods On Polygonal And Polyhedral Meshes
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| Author | : Andrea Cangiani |
| Publisher | : Springer |
| Total Pages | : 133 |
| Release | : 2017-11-27 |
| Genre | : Mathematics |
| ISBN | : 3319676733 |
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.
| Author | : Daniele Antonio Di Pietro |
| Publisher | : Springer Nature |
| Total Pages | : 342 |
| Release | : 2021-06-14 |
| Genre | : Mathematics |
| ISBN | : 3030693635 |
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.
| Author | : Daniele Antonio Di Pietro |
| Publisher | : Springer Nature |
| Total Pages | : 552 |
| Release | : 2020-04-03 |
| Genre | : Mathematics |
| ISBN | : 3030372030 |
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.
| Author | : Giulio Ventura |
| Publisher | : Springer |
| Total Pages | : 272 |
| Release | : 2016-08-24 |
| Genre | : Technology & Engineering |
| ISBN | : 3319412469 |
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.
| Author | : Matteo Cicuttin |
| Publisher | : Springer Nature |
| Total Pages | : 138 |
| Release | : 2021-11-11 |
| Genre | : Mathematics |
| ISBN | : 3030814777 |
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 | : Jens M. Melenk |
| Publisher | : Springer Nature |
| Total Pages | : 571 |
| Release | : 2023-06-30 |
| Genre | : Mathematics |
| ISBN | : 3031204328 |
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.
| Author | : Rubén Sevilla |
| Publisher | : Springer Nature |
| Total Pages | : 328 |
| Release | : 2022-05-18 |
| Genre | : Mathematics |
| ISBN | : 3030925404 |
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.
| Author | : Kai Hormann |
| Publisher | : CRC Press |
| Total Pages | : 351 |
| Release | : 2017-10-30 |
| Genre | : Computers |
| ISBN | : 1498763618 |
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
| Author | : Susanne C. Brenner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 364 |
| Release | : 2020-07-29 |
| Genre | : Education |
| ISBN | : 1470451638 |
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.
| Author | : Hong Shen |
| Publisher | : Springer Nature |
| Total Pages | : 643 |
| Release | : 2022-03-15 |
| Genre | : Computers |
| ISBN | : 3030967727 |
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.
