Computational Electrodynamics

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).