High Order Discontinuous Galerkin Methods For The Maxwell Equations

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High-order Discontinuous Galerkin Methods for the Maxwell Equations

Author : Hassan Fahs
Publisher : Omniscriptum
ISBN 13 : 9786131500206
Total Pages : 208 pages
Book Rating : 4.5/5 (2 download)

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Book Synopsis High-order Discontinuous Galerkin Methods for the Maxwell Equations by : Hassan Fahs

Download or read book High-order Discontinuous Galerkin Methods for the Maxwell Equations written by Hassan Fahs and published by Omniscriptum. This book was released on 2018-02-28 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the calculation of the numerical flux at an interface between neighbouring elements, and a second-order leap-frog time integration scheme. Next, to reduce the computational costs of the method, we propose a hp-like DGTD method which combines local h-refinement and p-enrichment. Then, we report on a detailed numerical evaluation of the DGTD methods using several propagation problems. Finally, in order to improve the accuracy and rate of convergence of the DGTD methods previously studied, we study a family of high-order explicit leap-frog time schemes. These time schemes ensure the stability under some CFL-like condition. We also establish rigorously the convergence of the semi-discrete approximation to Maxwell's equations and we provide bounds on the global divergence error.

Nodal Discontinuous Galerkin Methods

Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
ISBN 13 : 0387720650
Total Pages : 507 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Nodal Discontinuous Galerkin Methods by : Jan S. Hesthaven

Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.

Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations

Author : Gary Cohen
Publisher : Springer
ISBN 13 : 9401777616
Total Pages : 393 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations by : Gary Cohen

Download or read book Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations written by Gary Cohen and published by Springer. This book was released on 2016-08-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.

Nodal Discontinuous Galerkin Methods

Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
ISBN 13 : 0387720677
Total Pages : 502 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Nodal Discontinuous Galerkin Methods by : Jan S. Hesthaven

Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.

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

Author : Mejdi Azaïez
Publisher : Springer Science & Business Media
ISBN 13 : 3319016016
Total Pages : 421 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 by : Mejdi Azaïez

Download or read book Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 written by Mejdi Azaïez and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 421 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 (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.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Author : Spencer J. Sherwin
Publisher : Springer Nature
ISBN 13 : 3030396479
Total Pages : 658 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 by : Spencer J. Sherwin

Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 written by Spencer J. Sherwin and published by Springer Nature. This book was released on 2020-08-11 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations

Author : Beatrice Riviere
Publisher : SIAM
ISBN 13 : 089871656X
Total Pages : 201 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations by : Beatrice Riviere

Download or read book Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations written by Beatrice Riviere and published by SIAM. This book was released on 2008-12-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.

Discontinuous Galerkin Methods

Author : Bernardo Cockburn
Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn

Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Finite Element Methods for Maxwell's Equations

Author : Peter Monk
Publisher : Clarendon Press
ISBN 13 : 0191545228
Total Pages : 468 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Finite Element Methods for Maxwell's Equations by : Peter Monk

Download or read book Finite Element Methods for Maxwell's Equations written by Peter Monk and published by Clarendon Press. This book was released on 2003-04-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.

High-order Runge-Kutta Discontinuous Galerkin Methods for Computational Electromagnetics

Author : Min-Hung Chen
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis High-order Runge-Kutta Discontinuous Galerkin Methods for Computational Electromagnetics by : Min-Hung Chen

Download or read book High-order Runge-Kutta Discontinuous Galerkin Methods for Computational Electromagnetics written by Min-Hung Chen and published by . This book was released on 2005 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Author : Jens M. Melenk
Publisher : Springer Nature
ISBN 13 : 3031204328
Total Pages : 571 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by : Jens M. Melenk

Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 written by Jens M. Melenk and published by Springer Nature. This book was released on 2023-06-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Author : Marco L. Bittencourt
Publisher : Springer
ISBN 13 : 3319658700
Total Pages : 681 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 by : Marco L. Bittencourt

Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 written by Marco L. Bittencourt and published by Springer. This book was released on 2017-11-07 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), 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.

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

Author : Jichun Li
Publisher : Springer Science & Business Media
ISBN 13 : 3642337899
Total Pages : 309 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials by : Jichun Li

Download or read book Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials written by Jichun Li and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.

Spectral and High Order Methods for Partial Differential Equations

Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
ISBN 13 : 3642153372
Total Pages : 507 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations by : Jan S. Hesthaven

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.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

Author : Robert M. Kirby
Publisher : Springer
ISBN 13 : 3319198009
Total Pages : 504 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 by : Robert M. Kirby

Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 written by Robert M. Kirby and published by Springer. This book was released on 2015-11-26 with total page 504 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 (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.

Finite Elements II

Author : Alexandre Ern
Publisher : Springer Nature
ISBN 13 : 3030569233
Total Pages : 491 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Finite Elements II by : Alexandre Ern

Download or read book Finite Elements II written by Alexandre Ern and published by Springer Nature. This book was released on 2021-04-22 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computer Simulation Using Particles

Author : R.W Hockney
Publisher : CRC Press
ISBN 13 : 9781439822050
Total Pages : 566 pages
Book Rating : 4.8/5 (22 download)

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Book Synopsis Computer Simulation Using Particles by : R.W Hockney

Download or read book Computer Simulation Using Particles written by R.W Hockney and published by CRC Press. This book was released on 2021-03-24 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer simulation of systems has become an important tool in scientific research and engineering design, including the simulation of systems through the motion of their constituent particles. Important examples of this are the motion of stars in galaxies, ions in hot gas plasmas, electrons in semiconductor devices, and atoms in solids and liquids. The behavior of the system is studied by programming into the computer a model of the system and then performing experiments with this model. New scientific insight is obtained by observing such computer experiments, often for controlled conditions that are not accessible in the laboratory. Computer Simulation using Particles deals with the simulation of systems by following the motion of their constituent particles. This book provides an introduction to simulation using particles based on the NGP, CIC, and P3M algorithms and the programming principles that assist with the preparations of large simulation programs based on the OLYMPUS methodology. It also includes case study examples in the fields of astrophysics, plasmas, semiconductors, and ionic solids as well as more detailed mathematical treatment of the models, such as their errors, dispersion, and optimization. This resource will help you understand how engineering design can be assisted by the ability to predict performance using the computer model before embarking on costly and time-consuming manufacture.