Handbook of numerical analysis. Special volume-- numerical methods in electromagnetics / Volume XIII, (2005)

• Record Type: Book
• Other Titles: Numerical methods in electromagnetics
• Further Information: Note: Guest editors, W.H.A. Schilders, E.J.W. ter Matern.
• Other Names: Schilders, W. H. A; Ter Maten, E. Jan W
• Contents: Front cover ; copyright ; front matter ; General Preface; Preface; Contents of Volume XIII; Contents of the Handbook; Introduction to Electromagnetism; List of symbols; Preface; The microscopic Maxwell equations; Potentials and fields, the Lagrangian; The macroscopic Maxwell equations; Wave guides and transmission lines; From macroscopic field theory to electric circuits; Gauge conditions; The geometry of electrodynamics; Outlook; Acknowledgements; Integral theorems; Vector identities; References; body. Discretization of Electromagnetic Problems: The ``Generalized Finite Differences'' ApproachChapter I: Preliminatires: Euclidean Space ; Chapter II: Rewriting the Maxwell Equations ; Chapter III: Discretizing ; Chapter IV: Finite Elements ; References 1; Finite-Difference Time-Domain Methods; Introduction 2; Maxwell's equations; The Yee algorithm; Nonuniform Yee grid; Alternative finite-difference grids; Numerical dispersion; Algorithms for improved numerical dispersion; Numerical stability; Introduction; Complex-frequency analysis; Stable range: 0<=xi<=1; Unstable range: 1 <xi<xiupper bound. Example of calculating a stability bound: 3D cubic-cell latticeCourant factor normalization and extension to 2D and 1D grids; Examples of calculations involving numerical instability in a 1D grid; Example of calculation involving numerical instability in a 2D grid; Linear instability when the normalized Courant factor equals 1; Generalized stability problem; Boundary conditions; Variable and unstructured meshing; Lossy, dispersive, nonlinear, and gain materials; Alternating-direction-implicit time-stepping algorithm for operation beyond the Courant limit; Introduction. Formulation of the Zheng et al. algorithmUnsimplified system of time-stepping equations; Subiteration 1; Subiteration 2; Simplified system of time-stepping equations; Subiteration 1; Subiteration 2; Proof of numerical stability; Numerical dispersion; Additional accuracy limitations and their implications; Perfectly matched layer absorbing boundary conditions; Introduction to absorbing boundary conditions; Introduction to impedance-matched absorbing layers; Berenger's perfectly matched layer; Two-dimensional TEz case; Field-splitting modification of Maxwell's equations. Plane-wave solution within the Berenger mediumReflectionless matching condition; Structure of an FDTD grid employing Berenger's PML ABC; Two-dimensional TMz case; Three-dimensional case; Stretched-coordinate formulation of Berenger's PML; An anisotropic PML absorbing medium; Perfectly matched uniaxial medium; Relationship to Berenger's split-field PML; A generalized three-dimensional formulation; Inhomogeneous media; Theoretical performance of the PML; The continuous space; The discrete space; Grading of the PML loss parameters; Polynomial grading; Geometric grading; Discretization error.
• Publisher Details: Amsterdam Boston : Elsevier North-Holland
• Publication Date: 2005
• Extent: 1 online resource (1 volume)
• Subjects: 518; Electromagnetism -- Mathematical models; Electromagnetism -- Mathematical models; Numerical analysis; MATHEMATICS -- Numerical Analysis; Electromagnetism -- Mathematical models; Electronic books
• Languages: English
• ISBNs: 0080459153; 9780080459158
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.