Cai W. Computational Methods for Electromagnetic Phenomena

Cambridge University Press, Cambridge, 2013. — 464 p. — ISBN: 978-1-107-02105-1.A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nano-electronics, and plasmas.
The state-of-the-art numerical methods described include:
• Statistical fluctuation formulae for dielectric constants
• Particle mesh Ewald, fast multipole method, and image-based reaction field methods for long-range interactions
• High-order singular/hyper-singular (Nyström collocation/Galerkin) boundary and volume integral methods in layered media for Poisson–Boltzmann electro-statics, electromagnetic wave scattering, and electron density waves in quantum dots
• Absorbing and UPML boundary conditions
• High-order hierarchical N´ ed´ elec edge elements
• High-order discontinuous Galerkin (DG) and Yee scheme time-domain methods
• Finite element and plane wave frequency-domain methods for periodic structures
• Generalized DG beam propagation methods for optical waveguides
• NEGF (non-equilibrium Green’s function) and Wigner kinetic methods for quantum transport
• High-order WENO, Godunov and central schemes for hydrodynamic transport
• Vlasov–Fokker–Planck, PIC, and constrained MHD transport in plasmas