Finite Element And Discontinuous Galerkin Methods For Transient Wave Equations
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Finite Element And Discontinuous Galerkin Methods For Transient Wave Equations
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Author : Gary Cohen
language : en
Publisher: Springer
Release Date : 2016-08-05
Finite Element And Discontinuous Galerkin Methods For Transient Wave Equations written by Gary Cohen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Technology & Engineering categories.
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
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Author : Jan S. Hesthaven
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-18
Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-18 with Mathematics categories.
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.
Direct And Inverse Problems In Wave Propagation And Applications
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Author : Ivan Graham
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-14
Direct And Inverse Problems In Wave Propagation And Applications written by Ivan Graham and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Mathematics categories.
This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.
Frontiers In Numerical Analysis Durham 2010
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Author : James Blowey
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-10
Frontiers In Numerical Analysis Durham 2010 written by James Blowey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-10 with Mathematics categories.
This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.
Large Scale Structures In Acoustics And Electromagnetics
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1996-05-05
Large Scale Structures In Acoustics And Electromagnetics written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-05 with Science categories.
This book focuses on computational methods to determine the dynamics of large-scale electromagnetic, acoustic, and mechanical systems, including those with many substructures and characterized by an extended range of scales. Examples include large naval and maritime vessels, aerospace vehicles, and densely packed microelectronic and optical integrated circuits (VLSI). The interplay of time and frequency-domain computational and experimental procedures was addressed, emphasizing their relationship and synergy, and indicating mathematics research opportunities.
Deterministic Stochastic And Deep Learning Methods For Computational Electromagnetics
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Author : Wei Cai
language : en
Publisher: Springer Nature
Release Date : 2025-03-02
Deterministic Stochastic And Deep Learning Methods For Computational Electromagnetics written by Wei Cai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-02 with Mathematics categories.
This book provides a well-balanced and comprehensive picture based on clear physics, solid mathematical formulation, and state-of-the-art useful numerical methods in deterministic, stochastic, deep neural network machine learning approaches for computer simulations of electromagnetic and transport processes in biology, microwave and optical wave devices, and nano-electronics. Computational research has become strongly influenced by interactions from many different areas including biology, physics, chemistry, engineering, etc. A multifaceted approach addressing the interconnection among mathematical algorithms and physical foundation and application is much needed to prepare graduate students and researchers in applied mathematics and sciences and engineering for innovative advanced computational research in many applications areas, such as biomolecular solvation in solvents, radar wave scattering, the interaction of lights with plasmonic materials, plasma physics, quantum dots, electronic structure, current flows in nano-electronics, and microchip designs, etc.
Decomposition Methods For Differential Equations
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Author : Juergen Geiser
language : en
Publisher: CRC Press
Release Date : 2009-05-20
Decomposition Methods For Differential Equations written by Juergen Geiser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-20 with Mathematics categories.
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and num
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014
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Author : Robert M. Kirby
language : en
Publisher: Springer
Release Date : 2015-11-26
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014 written by Robert M. Kirby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Computers categories.
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.
Computational Fluid Dynamics Analysis Simulations And Applications
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Author : Mahboub Baccouch
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-02-26
Computational Fluid Dynamics Analysis Simulations And Applications written by Mahboub Baccouch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-26 with Science categories.
This book comprehensively explores numerical methods and their applications across diverse fields, strongly focusing on computational fluid dynamics (CFD) and advanced modeling techniques. Starting with numerical approaches for solving the viscid and inviscid Burgers equations establishes a foundation for understanding complex fluid dynamics. Subsequent chapters delve into cutting-edge topics, including Large Eddy Simulations (LES) for turbulence modeling, heat transfer analysis, and the influence of working fluids on vortex dynamics in industrial pipelines. The book also explores emerging areas such as nanoscale simulations, plasmonic excitations, and biomedical applications like hemodynamics in atrial fibrillation. Real-world case studies and practical examples demonstrate the versatility of CFD in addressing challenges in engineering, biology, and energy systems. This book combines theoretical rigour with practical insights and is designed for advanced undergraduate and graduate students, researchers, and professionals. It bridges the gap between numerical theory and real-world applications, providing readers with the tools to solve complex problems across various scientific and engineering domains. Whether you’re looking to deepen your understanding of numerical methods, enhance your CFD expertise, or explore innovative applications, this book is a valuable resource for gaining actionable insights and fostering innovation in computational modeling.
Time Domain Finite Element Methods For Maxwell S Equations In Metamaterials
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Author : Jichun Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-15
Time Domain Finite Element Methods For Maxwell S Equations In Metamaterials written by Jichun Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-15 with Computers categories.
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.