Download or read book Stability of Finite Element Solutions to Maxwell Equations in Frequency Domain written by Christoph Schwarzbach and published by . This book was released on 2009 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability of Finite Element Solutions to Maxwell s Equations in Frequency Domain written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics of time-harmonic electromagnetic phenomena can be mathematically described by boundary value problems. A standard approach is based on the vector Helmholtz equation in terms of the electric field. The curl operator involved has a large, non-trivial kernel which leads to an instable solution behaviour at low frequencies. If the boundary value problem is solved approximately using, e. g., the finite element method, the instability expresses itself by a badly conditioned coefficient matrix of the ensuing system of linear equations. A stable formulation is obtained by taking the continuity equation explicitly into account. In order to solve the boundary value problem numerically a finite element software package has been implemented. Its features comprise, amongst others, the treatment of unstructured meshes and piecewise polynomial, anisotropic constitutive parameters as well as the extension of Maxwell's equations to the Perfectly Matched Layer. Successful application of the software is demonstrated with examples from marine geophysics. In particular, the incorporation of seafloor topography by a continuous surface triangulation illustrates the geometric flexibility of the software.

Download or read book Stability of Finite Element Solutions to Maxwell Equations in Frequency Domain written by Christoph Schwarzbach and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Finite Element Time Domain Techniques for Maxwell s Equations Based on Differential Forms written by Joonshik Kim and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation is concerned with the development of numerical techniques for solving Maxwell equations in the time-domain. Two of the main challenges to obtain such solution are, first, how to construct explicit (that is, matrix-free) time-updating formulas without relinquishing the advantage of using irregular unstructured meshes in complex geometries, and second, how to best parallelize the algorithm to solve large-scale problems. The finite element time-domain (FETD) and the finite-difference time-Domain (FDTD) are presently the two most popular methods for solving Maxwell equations in the time-domain. FDTD employs a staggered-grid spatial discretization together with leap-frog style time update scheme to produce a method with many desirable properties such as: conservation of charge and energy, absence of spurious mode, and a simple easy-to-code algorithm. Nevertheless, FDTD (in its conventional form) relies on orthogonal grids, which is a disadvantage when modeling complex geometries. On the other hand, FETD is based upon unstructured grids and hence naturally tailored to handle complex geometries. However, in time-domain simulation (as opposed to frequency-domain simulations), FETD requires a matrix solver at every time step. Since the total number of time steps to produce the overall time-domain solution can be quite large, this requirement demands excessive computational resources. To overcome this problem, we develop a FETD algorithm with "FDTD-like" explicit characteristics. Usually, the system matrices generated after discretizing Maxwell equations in irregular grids are very large and sparse matrices, while their inverses are very large and dense matrices. To construct an explicit algorithm, ideally one would need to somehow obtain and use such inverses. However, these dense matrices are of course not useful in a update scheme because they are not only very costly to compute but also very costly to store for most practical problems. For this reason, we investigate the use of approximate sparse inverses to build update schemes for FETD. We show that the most direct choice, which is to use the approximate inverse of the system matrix itself, is not really an adequate choice because of the nature of the corresponding (continuum) operator, with long-range interactions. We therefore consider instead the use of the approximate inverse of the Hodge (or mass) matrix, which a symmetric positive definite matrix representing a strictly local operator in the continuum limit whose inverse is also local, to compute explicit update schemes. This entails the discretization of Maxwell's equations based on discrete differential forms and the use of a "mixed" set of basis functions for the FETD: Whitney one forms for the electric field intensity and Whitney two forms for the magnetic flux density. This choice of basis functions obeys a discrete version of the de Rham diagram and leads to solutions that are free of spurious modes and numerically stable. We construct a parallel approach to compute the approximate inverse, and provide an error analysis of the resulting solutions versus the density of the approximate inverse and the mesh refinement considered. A higher-order version of the mixed FETD algorithm is also constructed, showing good convergence versus the polynomial order.

Download or read book A Least squares Finite Element Method for Electromagnetic Scattering Problems written by Jie Wu and published by . This book was released on 1996 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regularized Maxwell Equations and Nodal Finite Elements for Electromagnetic Field Computations in Frequency Domain written by Rubén Otín Fortuño and published by . This book was released on 2011 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Finite Element Method in Electromagnetics written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2015-02-18 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

Download or read book Finite Element and Finite Difference Methods in Electromagnetic Scattering written by M.A. Morgan and published by Elsevier. This book was released on 2013-10-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled scalar potentials, to the consideration of conforming boundary elements and leap-frog time-marching in transient field problems involving corners and wedges in two and three dimensions, the volume will provide an indispensable reference source for practitioners and students of computational electromagnetics.

Download or read book A Finite Element Perspective in Analyzing Maxwell s Equation written by Thomas Korjack and published by . This book was released on 1999 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of the three-dimensional (3-D) finite element formulation of Maxwell's equations governing classical electromagnetic propagation in dielectrics is given including its analogy to Navier's equation. The weak form of the electric field equation is reviewed along with dispersion analysis and approximation equations. Radiation boundary conditions are also explored to include paraxial absorber, Sandier absorber, and other absorber comparisons. In addition, time domains vs. frequency domains are investigated with a listing of possible advantages and disadvantages. It was concluded that if large-scale calculations need to be done today, time-domain techniques provide the most practicable means; however, it is still premature to promote such solvers as production level tools for engineers.

Download or read book A Parallel Direct Method for Finite Element Electromagnetic Computations Based on Domain Decomposition written by Javad Moshfegh and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: High performance parallel computing and direct (factorization-based) solution methods have been the two main trends in electromagnetic computations in recent years. When time-harmonic (frequency-domain) Maxwell's equation are directly discretized with the Finite Element Method (FEM) or other Partial Differential Equation (PDE) methods, the resulting linear system of equations is sparse and indefinite, thus harder to efficiently factorize serially or in parallel than alternative methods e.g. integral equation solutions, that result in dense linear systems. State-of-the-art sparse matrix direct solvers such as MUMPS and PARDISO don't scale favorably, have low parallel efficiency and high memory footprint. This work introduces a new class of sparse direct solvers based on domain decomposition method, termed Direct Domain Decomposition Method (D3M), which is reliable, memory efficient, and offers very good parallel scalability for arbitrary 3D FEM problems. Unlike recent trends in approximate/low-rank solvers, this method focuses on `numerically exact' solution methods as they are more reliable for complex `real-life' models. The proposed method leverages physical insights at every stage of the development through a new symmetric domain decomposition method (DDM) with one set of Lagrange multipliers. Applying a special regularization scheme at the interfaces, either artificial loss or gain is introduced to each domain to eliminate non-physical internal resonances. A block-wise recursive algorithm based on Takahashi relationship is proposed for the efficient computation of discrete Dirichlet-to-Neumann (DtN) map to reduce the volumetric problem from all domains into an auxiliary surfacial problem defined on the domain interfaces only. Numerical results show up to 50% run-time saving in DtN map computation using the proposed block-wise recursive algorithm compared to alternative approaches. The auxiliary unknowns on the domain interfaces form a considerably (approximately an order of magnitude) smaller block-wise sparse matrix, which is efficiently factorized using a customized block LDL$^T$ factorization with restricted pivoting to ensure stability. The parallelization of the proposed D3M is realized based on Directed Acyclic Graph (DAG). Recent advances in parallel dense direct solvers, have shifted toward parallel implementation that rely on DAG scheduling to achieve highly efficient asynchronous parallel execution. However, adaptation of such schemes to sparse matrices is harder and often impractical. In D3M, computation of each domain's discrete DtN map ``embarrassingly parallel'', whereas the customized block LDLT is suitable for a block directed acyclic graph (B-DAG) task scheduling, similar to that used in dense matrix parallel direct solvers. In this approach, computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix blocks of the reduced matrix. These tasks can be statically scheduled for parallel execution using their DAG dependencies and weights that depend on estimates of computation and communication costs. Comparisons with state-of-the-art exact direct solvers on electrically large problems suggest up to 20% better parallel efficiency, 30% - 3X less memory and slightly faster in runtime, while maintaining the same accuracy.

Download or read book Electromagnetic Analysis and Design in Magnetic Resonance Imaging written by Jianming Jin and published by Routledge. This book was released on 2018-02-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive treatment of electromagnetic analysis and design of three critical devices for an MRI system - the magnet, gradient coils, and radiofrequency (RF) coils. Electromagnetic Analysis and Design in Magnetic Resonance Imaging is unique in its detailed examination of the analysis and design of the hardware for an MRI system. It takes an engineering perspective to serve the many scientists and engineers in this rapidly expanding field. Chapters present: an introduction to MRI basic concepts of electromagnetics, including Helmholtz and Maxwell coils, inductance calculation, and magnetic fields produced by special cylindrical and spherical surface currents principles for the analysis and design of gradient coils, including discrete wires and the target field method analysis of RF coils based on the equivalent lumped-circuit model as well as an analysis based on the integral equation formulation survey of special purpose RF coils analytical and numerical methods for the analysis of electromagnetic fields in biological objects With the continued, active development of MRI instrumentation, Electromagnetic Analysis and Design in Magnetic Resonance Imaging presents an excellent, logically organized text - an indispensable resource for engineers, physicists, and graduate students working in the field of MRI.

Download or read book The Least Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Download or read book Computational Electromagnetics written by Anders Bondeson and published by Springer Science & Business Media. This book was released on 2006-02-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included

Download or read book Foundations of Geophysical Electromagnetic Theory and Methods written by Michael S Zhdanov and published by Elsevier. This book was released on 2017-10-26 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Geophysical Electromagnetic Theory and Methods, Second Edition, builds on the strength of the first edition to offer a systematic exposition of geophysical electromagnetic theory and methods. This new edition highlights progress made over the last decade, with a special focus on recent advances in marine and airborne electromagnetic methods. Also included are recent case histories on practical applications in tectonic studies, mineral exploration, environmental studies and off-shore hydrocarbon exploration. The book is ideal for geoscientists working in all areas of geophysics, including exploration geophysics and applied physics, as well as graduate students and researchers working in the field of electromagnetic theory and methods. Presents theoretical and methodological foundations of geophysical field theory Synthesizes fundamental theory and the most recent achievements of electromagnetic (EM) geophysical methods in the framework of a unified systematic exposition Offers a unique breadth and completeness in providing a general picture of the current state-of-the-art in EM geophysical technology Discusses practical aspects of EM exploration for mineral and energy resources

Download or read book Development of a Time Domain Hybrid Finite Difference finite Element Method for Solutions to Maxwell s Equations in Anisotropic Media written by Christopher W. Kung and published by . This book was released on 2009 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The finite difference time domain (FDTD) and finite element numerical methods are two popular time domain computational methods in electromagnetics, but the two numerical methods have certain tradeoffs. FDTD is a fast explicit method with second order accuracy, but the method's accuracy is reduced when analyzing structures that are not conforming to a Cartesian grid. The finite element method on the other hand excels at examining domains with non-conforming structures, but its method of solution usually requires a matrix inverse operation, which is computationally expensive. Fortunately, research in hybrid methods have shown that the FDTD method for isotropic materials can be viewed upon as a subset of finite elements, and from this viewpoint, the FDTD and finite element method in the time domain can be hybridized together to the advantages of both methods while mitigating the disadvantages.

Download or read book Numerical Time Dependent Partial Differential Equations for Scientists and Engineers written by Moysey Brio and published by Academic Press. This book was released on 2010-09-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations