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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

2017-11-27 Mathematics
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Release : 2017-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 733/5 ( reviews)

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Book Synopsis hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes by : Andrea Cangiani

Download or read book hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes written by Andrea Cangiani. This book was released on 2017-11-27. Available in PDF, EPUB and Kindle. Book excerpt: 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

2021-06-14 Mathematics
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Release : 2021-06-14
Genre : Mathematics
Kind : eBook
Book Rating : 635/5 ( reviews)

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Book Synopsis Polyhedral Methods in Geosciences by : Daniele Antonio Di Pietro

Download or read book Polyhedral Methods in Geosciences written by Daniele Antonio Di Pietro. This book was released on 2021-06-14. Available in PDF, EPUB and Kindle. Book excerpt: 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

2020-04-03 Mathematics
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Release : 2020-04-03
Genre : Mathematics
Kind : eBook
Book Rating : 030/5 ( reviews)

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Book Synopsis The Hybrid High-Order Method for Polytopal Meshes by : Daniele Antonio Di Pietro

Download or read book The Hybrid High-Order Method for Polytopal Meshes written by Daniele Antonio Di Pietro. This book was released on 2020-04-03. Available in PDF, EPUB and Kindle. Book excerpt: 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

2016-08-24 Technology & Engineering
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Release : 2016-08-24
Genre : Technology & Engineering
Kind : eBook
Book Rating : 469/5 ( reviews)

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Book Synopsis Advances in Discretization Methods by : Giulio Ventura

Download or read book Advances in Discretization Methods written by Giulio Ventura. This book was released on 2016-08-24. Available in PDF, EPUB and Kindle. Book excerpt: 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

2021-11-11 Mathematics
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Release : 2021-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 777/5 ( reviews)

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Book Synopsis Hybrid High-Order Methods by : Matteo Cicuttin

Download or read book Hybrid High-Order Methods written by Matteo Cicuttin. This book was released on 2021-11-11. 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.

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