Mathematical Foundations Of Computational Electromagnetism
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Mathematical Foundations Of Computational Electromagnetism
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Author : Franck Assous
language : en
Publisher: Springer
Release Date : 2018-06-09
Mathematical Foundations Of Computational Electromagnetism written by Franck Assous and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-09 with Mathematics categories.
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Computational Electromagnetism
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Author : Houssem Haddar
language : en
Publisher: Springer
Release Date : 2015-07-20
Computational Electromagnetism written by Houssem Haddar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-20 with Mathematics categories.
Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.
Foundations Of Computational Mathematics Budapest 2011
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Author : Society for the Foundation of Computational Mathematics
language : en
Publisher: Cambridge University Press
Release Date : 2013
Foundations Of Computational Mathematics Budapest 2011 written by Society for the Foundation of Computational Mathematics and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.
Foundations Of Computational Mathematics Santander 2005
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Author : Society for the Foundation of Computational Mathematics
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-29
Foundations Of Computational Mathematics Santander 2005 written by Society for the Foundation of Computational Mathematics and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-29 with Mathematics categories.
Surveys and summaries of latest research in numerical analysis, optimization, computer algebra and scientific computing.
Mathematical Analysis And Simulation Of Field Models In Accelerator Circuits
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Author : Idoia Cortes Garcia
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Mathematical Analysis And Simulation Of Field Models In Accelerator Circuits written by Idoia Cortes Garcia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Technology & Engineering categories.
This book deals with the analysis and development of numerical methods for the time-domain analysis of multiphysical effects in superconducting circuits of particle accelerator magnets. An important challenge is the simulation of “quenching”, i.e. the transition of a material from the superconducting to the normally electrically conductive state. The book analyses complex mathematical structures and presents models to simulate such quenching events in the context of generalized circuit elements. Furthermore, it proposes efficient parallelized algorithms with guaranteed convergence properties for the simulation of multiphysical problems. Spanning from theoretical concepts to applied research, and featuring rigorous mathematical presentations on one side, as well as simplified explanations of many complex issues, on the other side, this book provides graduate students and researchers with a comprehensive introduction on the state of the art and a source of inspiration for future research. Moreover, the proposed concepts and methods can be extended to the simulation of multiphysical phenomena in different application contexts.
Finite Elements Ii
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Author : Alexandre Ern
language : en
Publisher: Springer Nature
Release Date : 2021-04-22
Finite Elements Ii written by Alexandre Ern and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-22 with Mathematics categories.
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.
Explorations In Computational Physics
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Author : Devang Patil
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Explorations In Computational Physics written by Devang Patil and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Explorations in Computational Physics" delves into the intricate world of computational physics, offering a comprehensive guide from fundamental theories to cutting-edge applications. This book serves as an indispensable companion for both novice learners and seasoned researchers. We cover a diverse array of topics, meticulously unfolding layers of computational techniques and their applications in various branches of physics. From classical mechanics simulations elucidating celestial mechanics to quantum mechanics computations unraveling atomic and subatomic realms, the book navigates through the vast landscape of computational methodologies with clarity and precision. Furthermore, we delve into electromagnetic field simulations, statistical mechanics, and thermodynamics, equipping readers with tools to model complex physical phenomena with accuracy and efficiency. High-performance computing techniques, data analysis, and visualization methodologies are elucidated, empowering readers to harness modern computational resources in their research. With lucid explanations, illustrative examples, and insightful discussions on emerging technologies like quantum computing and artificial intelligence, "Explorations in Computational Physics" fosters a deeper understanding of computational methodologies and their transformative impact on physics research.
Electromagnetic Theory And Computation
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Author : Paul W. Gross
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-14
Electromagnetic Theory And Computation written by Paul W. Gross and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-14 with Mathematics categories.
This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. The connection between topology and electromagnetism has been known since the 19th century, but there has been little exposition of its relevance to computational methods in modern topological language. This book is an effort to close that gap. It will be of interest to people working in finite element methods for electromagnetic computation and those who have an interest in numerical and industrial applications of algebraic topology.
Computational Electromagnetism
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Author : Alain Bossavit
language : en
Publisher: Academic Press
Release Date : 1998-02-04
Computational Electromagnetism written by Alain Bossavit and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-04 with Science categories.
Computational Electromagnetism refers to the modern concept of computer-aided analysis, and design, of virtually all electric devices such as motors, machines, transformers, etc., as well as of the equipment inthe currently booming field of telecommunications, such as antennas, radars, etc. The present book is uniquely written to enable the reader-- be it a student, a scientist, or a practitioner-- to successfully perform important simulation techniques and to design efficient computer software for electromagnetic device analysis. Numerous illustrations, solved exercises, original ideas, and an extensive and up-to-date bibliography make it a valuable reference for both experts and beginners in the field. A researcher and practitioner will find in it information rarely available in other sources, such as on symmetry, bilateral error bounds by complimentarity, edge and face elements, treatment of infinite domains, etc. At the same time, the book is a useful teaching tool for courses in computational techniques in certain fields of physics and electrical engineering. As a self-contained text, it presents an extensive coverage of the most important concepts from Maxwells equations to computer-solvable algebraic systems-- for both static, quasi-static, and harmonic high-frequency problems.BenefitsTo the EngineerA sound background necessary not only to understand the principles behind variational methods and finite elements, but also to design pertinent and well-structured software.To the Specialist in Numerical ModelingThe book offers new perspectives of practical importance on classical issues: the underlying symmetry of Maxwell equations, their interaction with other fields of physics in real-life modeling, the benefits of edge and face elements, approaches to error analysis, and "complementarity."To the TeacherAn expository strategy that will allow you to guide the student along a safe and easy route through otherwise difficult concepts: weak formulations and their relation to fundamental conservation principles of physics, functional spaces, Hilbert spaces, approximation principles, finite elements, and algorithms for solving linear systems. At a higher level, the book provides a concise and self-contained introduction to edge elements and their application to mathematical modeling of the basic electromagnetic phenomena, and static problems, such as eddy-current problems and microwaves in cavities.To the StudentSolved exercises, with "hint" and "full solution" sections, will both test and enhance the understanding of the material. Numerous illustrations will help in grasping difficult mathematical concepts.
Applications Of Differential Algebraic Equations Examples And Benchmarks
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Author : Stephen Campbell
language : en
Publisher: Springer
Release Date : 2019-06-08
Applications Of Differential Algebraic Equations Examples And Benchmarks written by Stephen Campbell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-08 with Mathematics categories.
This volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text. Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.