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# Maxwell's equations

About: Maxwell's equations is a research topic. Over the lifetime, 13741 publications have been published within this topic receiving 262049 citations. The topic is also known as: Maxwell equations & Maxwell's laws.

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Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.

13,304 citations

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31 May 1995

TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.

Abstract: Part 1 Reinventing electromagnetics: background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology. Part 2 The one-dimensional scalar wave equation: propagating wave solutions finite-difference approximation of the scalar wave equation dispersion relations for the one-dimensional wave equation numerical group velocity numerical stability. Part 3 Introduction to Maxwell's equations and the Yee algorithm: Maxwell's equations in three dimensions reduction to two dimensions equivalence to the wave equation in one dimension. Part 4 Numerical stability: TM mode time eigenvalue problem space eigenvalue problem extension to the full three-dimensional Yee algorithm. Part 5 Numerical dispersion: comparison with the ideal dispersion case reduction to the ideal dispersion case for special grid conditions dispersion-optimized basic Yee algorithm dispersion-optimized Yee algorithm with fourth-order accurate spatial differences. Part 6 Incident wave source conditions for free space and waveguides: requirements for the plane wave source condition the hard source total-field/scattered field formulation pure scattered field formulation choice of incident plane wave formulation. Part 7 Absorbing boundary conditions for free space and waveguides: Bayliss-Turkel scattered-wave annihilating operators Engquist-Majda one-way wave equations Higdon operator Liao extrapolation Mei-Fang superabsorption Berenger perfectly-matched layer (PML) absorbing boundary conditions for waveguides. Part 8 Near-to-far field transformation: obtaining phasor quantities via discrete fourier transformation surface equivalence theorem extension to three dimensions phasor domain. Part 9 Dispersive, nonlinear, and gain materials: linear isotropic case recursive convolution method linear gyrontropic case linear isotropic case auxiliary differential equation method, Lorentz gain media. Part 10 Local subcell models of the fine geometrical features: basis of contour-path FD-TD modelling the simplest contour-path subcell models the thin wire conformal modelling of curved surfaces the thin material sheet relativistic motion of PEC boundaries. Part 11 Explicit time-domain solution of Maxwell's equations using non-orthogonal and unstructured grids, Stephen Gedney and Faiza Lansing: nonuniform, orthogonal grids globally orthogonal global curvilinear co-ordinates irregular non-orthogonal unstructured grids analysis of printed circuit devices using the planar generalized Yee algorithm. Part 12 The body of revolution FD-TD algorithm, Thomas Jurgens and Gregory Saewert: field expansion difference equations for on-axis cells numerical stability PML absorbing boundary condition. Part 13 Modelling of electromagnetic fields in high-speed electronic circuits, Piket-May and Taflove. (part contents).

10,961 citations

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01 Jan 1992

TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).

Abstract: Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index

4,762 citations

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TL;DR: A fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis is described.

Abstract: We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that O Delta x;2 convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.

2,712 citations

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01 Jan 1983

TL;DR: In this article, the authors consider boundary value problems in Cylindrical Coordinates and present a solution to the problem of boundary addition and subtraction in Cartesian Coordinates.

Abstract: 1. The Electromagnetic Model. Introduction. The Electromagnetic Model. Si Units and Universal Constants. Review Questions. 2. Vector Analysis. Introduction. Vector Addition and Subtraction. Products of Vectors. Orthogonal Coordinate Systems. Integrals Containing Vector Functions. Gradient of a Scalar Field. Divergence of a Vector Field. Divergence Theorem. Curl of a Vector Field. Stoke's Theorem. Two Null Identities. Helmholtz's Theorem. Review Questions. Problems. 3. Static Electric Fields. Introduction. Fundamental Postulates of Electrostatics in Free Space. Coulomb's Law. Gauss's Law and Applications. Electric Potential. Conductors in Static Electric Field. Dielectrics in Static Electric Field. Electric Flux Density and Dielectric Constant. Boundary Conditions for Electrostatic Fields. Capacitances and Capacitors. Electrostatic Energy and Forces. Solution of Electrostatic Boundary-Value Problems. Review Questions. Problems. 4. Solution of Electrostatic Problems. Introduction. Poisson's and Laplaces' Equations. Uniqueness of Electrostatic Functions. Method of Images. Boundary-Value Problems in Cartesian Coordinates. Boundary-Value Problems in Cylindrical Coordinates. Boundary-Value Problems in Spherical Coordinates. Review Questions. Problems. 5. Steady Electric Currents. Introduction. Current Density and Ohm's Law. Electromotive Force and Kirchoff's Voltage Law. Equation of Continuity and Kirchoff's Current Law. Power Dissipation and Joule's Law. Boundary Conditions for Current Density. Resistance Calculations. Review Questions. Problems. 6. Static Magnetic Fields. Introduction. Fundamental Postulates of Magnetostatics in Free Space. Vector Magnetic Potential. The Biot-Savart Law and Applications. The Magnetic Dipole. Magnetization and Equivalent Current Densities. Magnetic Field Intensity and Relative Permeability. Magnetic Circuits. Behavior of Magnetic Materials. Boundary Conditions for Magnetostatic Fields. Inductances and Inductors. Magnetic Energy. Magnetic Forces and Torques. Review Questions. Problems. 7. Time-Varying Fields and Maxwell's Equations. Introduction. Faraday's Law of Electromagnetic Induction. Maxwell's Equations. Potential Functions. Electromagnetic Boundary Conditions. Wave Equations and their Solutions. Time-Harmonic Fields. Review Questions. Problems. 8. Plane Electromagnetic Waves. Introduction. Plane Waves in Lossless Media. Plane Waves in Lossy Media. Group Velocity. Flow of Electromagentic Power and the Poynting Vector. Normal Incidence of Plane Waves at a Plane Conducting Boundary. Oblique Incidence of Plane Waves at a Plane Conducting Boundary. Normal Incidence of Plane Waves at a Plane Dielectric Boundary. Normal Incidence of Plane Waves at Multiple Dielectric Interfaces. Oblique Incidence of Plane Waves at a Plane Dielectric Boundary. Review Questions. Problems. 9. Theory and Application of Transmission Lines Introduction. Transverse Electromagnetic Wave Along a Parallel-Plate. Transmission Line General Transmission-Line Equations. Wave Characteristics on Finite Transmission Lines. Transients on Transmission Lines. The Smith Chart. Transmission-Line Impedance Matching. Review Questions. Problems. 10. Waveguides and Cavity Resonators. Introduction. General Wave Behaviors Along Uniform Guiding Structures. Parallel-Plate Waveguide. Rectangular Waveguides. Circular Waveguides. Dielectric Waveguides. Cavity Resonators. Review Questions. Problems. 11. Antennas and Radiating Systems. Introduction. Radiation Fields of Elemental Dipoles. Antenna Patterns and Antenna Parameters. Thin Linear Antennas. Antenna Arrays. Receiving Antennas. Transmit-Receive Systems. Some Other Antenna Types. Review Questions. Problems. Appendix A: Symbols and Units. Appendix B: Some Useful Material Constants. Bibliography. Answers to Selected Problems. Index. Back Endpapers.

1,789 citations