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Author : Manuel Esteban Solano Palma
Publisher :
ISBN 13 :
Total Pages : 75 pages
Book Rating : 4.:/5 (778 download)
Download or read book Hybridizable Discontinuous Galerkin Method for Curved Domains written by Manuel Esteban Solano Palma and published by . This book was released on 2012 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Deepa Mahajan
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.:/5 (319 download)
Download or read book Boundary-conforming Discontinuous Galerkin Methods Via Extensions from Subdomains written by Deepa Mahajan and published by . This book was released on 2007 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrea Cangiani
Publisher : Springer
ISBN 13 : 3319676733
Total Pages : 133 pages
Book Rating : 4.3/5 (196 download)
Download or read book hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes written by Andrea Cangiani and published by Springer. This book was released on 2017-11-27 with total page 133 pages. 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.
Author : Giulio Ventura
Publisher : Springer
ISBN 13 : 3319412469
Total Pages : 272 pages
Book Rating : 4.3/5 (194 download)
Download or read book Advances in Discretization Methods written by Giulio Ventura and published by Springer. This book was released on 2016-08-24 with total page 272 pages. 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.
Author : Yu Zhu
Publisher : John Wiley & Sons
ISBN 13 : 0471786373
Total Pages : 438 pages
Book Rating : 4.4/5 (717 download)
Download or read book Multigrid Finite Element Methods for Electromagnetic Field Modeling written by Yu Zhu and published by John Wiley & Sons. This book was released on 2006-03-10 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive monograph that features state-of-the-art multigrid methods for enhancing the modeling versatility, numerical robustness, and computational efficiency of one of the most popular classes of numerical electromagnetic field modeling methods: the method of finite elements. The focus of the publication is the development of robust preconditioners for the iterative solution of electromagnetic field boundary value problems (BVPs) discretized by means of finite methods. Specifically, the authors set forth their own successful attempts to utilize concepts from multigrid and multilevel methods for the effective preconditioning of matrices resulting from the approximation of electromagnetic BVPs using finite methods. Following the authors' careful explanations and step-by-step instruction, readers can duplicate the authors' results and take advantage of today's state-of-the-art multigrid/multilevel preconditioners for finite element-based iterative electromagnetic field solvers. Among the highlights of coverage are: * Application of multigrid, multilevel, and hybrid multigrid/multilevel preconditioners to electromagnetic scattering and radiation problems * Broadband, robust numerical modeling of passive microwave components and circuits * Robust, finite element-based modal analysis of electromagnetic waveguides and cavities * Application of Krylov subspace-based methodologies for reduced-order macromodeling of electromagnetic devices and systems * Finite element modeling of electromagnetic waves in periodic structures The authors provide more than thirty detailed algorithms alongside pseudo-codes to assist readers with practical computer implementation. In addition, each chapter includes an applications section with helpful numerical examples that validate the authors' methodologies and demonstrate their computational efficiency and robustness. This groundbreaking book, with its coverage of an exciting new enabling computer-aided design technology, is an essential reference for computer programmers, designers, and engineers, as well as graduate students in engineering and applied physics.
Author : Lauren Nicole Kolkman
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (16 download)
Download or read book Implementation of an Implicit-explicit Scheme for Hybridizable Discontinuous Galerkin written by Lauren Nicole Kolkman and published by . This book was released on 2018 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods, specifically Hybridizable Discontinuous Galerkin (HDG), are used in many applications. One choice made when implementing HDG for a specific problem is whether time integration should be performed implicitly or explicitly. Both approaches have their advantages but, for some problems, a combination of these methods is a better choice than either on their own. Thus, an implicit-explicit (IMEX) scheme that splits the computational domain into implicit and explicit regions based on the domain geometry is considered in this thesis. This allows for stability throughout the domain and exploits the advantages each scheme has to offer. A study of the convergence and properties of this implementation of the IMEX method is presented along with comparisons to the individual methods.
Author : Fred J. Vermolen
Publisher : Springer Nature
ISBN 13 : 3030558746
Total Pages : 1185 pages
Book Rating : 4.0/5 (35 download)
Download or read book Numerical Mathematics and Advanced Applications ENUMATH 2019 written by Fred J. Vermolen and published by Springer Nature. This book was released on 2021-04-30 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, 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, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).
Author : Francis X. Giraldo
Publisher : Springer Nature
ISBN 13 : 3030550699
Total Pages : 559 pages
Book Rating : 4.0/5 (35 download)
Download or read book An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases written by Francis X. Giraldo and published by Springer Nature. This book was released on 2020-10-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.
Author : Shukai Du
Publisher : Springer Nature
ISBN 13 : 3030272303
Total Pages : 124 pages
Book Rating : 4.0/5 (32 download)
Download or read book An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method written by Shukai Du and published by Springer Nature. This book was released on 2019-08-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bo Dong
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (319 download)
Download or read book Superconvergent Discontinuous Galerkin Methods for Elliptic Problems written by Bo Dong and published by . This book was released on 2007 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniele Antonio Di Pietro
Publisher : Springer Nature
ISBN 13 : 3030693635
Total Pages : 342 pages
Book Rating : 4.0/5 (36 download)
Download or read book Polyhedral Methods in Geosciences written by Daniele Antonio Di Pietro and published by Springer Nature. This book was released on 2021-06-14 with total page 342 pages. 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.
Author : Matteo Cicuttin
Publisher : Springer Nature
ISBN 13 : 3030814777
Total Pages : 138 pages
Book Rating : 4.0/5 (38 download)
Download or read book Hybrid High-Order Methods written by Matteo Cicuttin and published by Springer Nature. This book was released on 2021-11-11 with total page 138 pages. 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.
Author : Martin Kronbichler
Publisher : Springer Nature
ISBN 13 : 3030606104
Total Pages : 314 pages
Book Rating : 4.0/5 (36 download)
Download or read book Efficient High-Order Discretizations for Computational Fluid Dynamics written by Martin Kronbichler and published by Springer Nature. This book was released on 2021-01-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.
Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
ISBN 13 : 3642153372
Total Pages : 507 pages
Book Rating : 4.6/5 (421 download)
Download or read book Spectral and High Order Methods for Partial Differential Equations written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : C.K. Birdsall
Publisher : CRC Press
ISBN 13 : 1482263068
Total Pages : 504 pages
Book Rating : 4.4/5 (822 download)
Download or read book Plasma Physics via Computer Simulation written by C.K. Birdsall and published by CRC Press. This book was released on 2018-10-08 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divided into three main parts, the book guides the reader to an understanding of the basic concepts in this fascinating field of research. Part 1 introduces you to the fundamental concepts of simulation. It examines one-dimensional electrostatic codes and electromagnetic codes, and describes the numerical methods and analysis. Part 2 explores the mathematics and physics behind the algorithms used in Part 1. In Part 3, the authors address some of the more complicated simulations in two and three dimensions. The book introduces projects to encourage practical work Readers can download plasma modeling and simulation software — the ES1 program — with implementations for PCs and Unix systems along with the original FORTRAN source code. Now available in paperback, Plasma Physics via Computer Simulation is an ideal complement to plasma physics courses and for self-study.
Author : Luming Wang
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (919 download)
Download or read book Discontinuous Galerkin Methods on Moving Domains with Large Deformations written by Luming Wang and published by . This book was released on 2015 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present two different numerical approaches for solving compressible flows on moving domains with high-order accuracy. The approaches are base on discontinuous Galerkin (DG) methods and are particularly designed for addressing the large deformation problems as the domain moves. A moving-mesh technique is first introduced to improve the mesh quality with the domain deforming. The technique moves the mesh nodes by DistMesh algorithm and locally changes the mesh topology by flipping edges or faces, which can be applied in both 2D and 3D. Moreover, some local density control operations are also developed to add or remove the mesh nodes to change the mesh adaptivity. Our first numerical scheme is formulated on a space-time framework using a nodal DG discretization on space-time domains with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. Along with the numerical scheme, two efficient algorithms for constructing globally conforming space-time slab meshes are given, based on our moving-mesh technique. The second approach employs DG discreatization with arbitrary-Eulerian-Lagrangian (ALE) framework by solving equations based on smooth mappings. An efficient local L2 projection is used for transferring solutions when mesh topology change happens. We test our two approaches by a number of numerical cases in both 2D and 3D. The tests involve convergence tests as well as simulations of laminar flows, which shows that the proposed methods achieve high-order accuracy and are able to handle problems with complex geometric motions.
Author : Alfio Quarteroni
Publisher : Springer
ISBN 13 : 3319020900
Total Pages : 338 pages
Book Rating : 4.3/5 (19 download)
Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.
