Computational Methods for Electromagnetic Phenomena

by Cai, Wei

• ISBN13: 9781107021051
• ISBN10: 1107021057
• Format: Hardcover
• Copyright: 2013-02-25
• Publisher: Cambridge Univ Pr

Summary

A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, micro-to-optical waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: • Statistical fluctuation formula for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions • High order singular/hypersingular (Nyström collocation/Galerkin) boundary and volume integral methods in layered media for Poisson–Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots • Absorbing and UPML boundary conditions • High order hierarchical Nédélec edge elements • High order discontinuous Galerkin (DG) and Yee finite difference time-domain methods • Finite element and plane wave frequency-domain methods for periodic structures • Generalized DG beam propagation method for optical waveguides • NEGF(Non-equilibrium Green's function) and Wigner kinetic methods for quantum transport • High order WENO and Godunov and central schemes for hydrodynamics transport • Vlasov-Fokker-Planck and PIC and constrained MHD transport in plasmas

Table of Contents

Electrostatics in Solvations

Dielectric constant and fluctuation formulae for molecular dynamics

Poisson-Boltzmann electrostatics and analytical approximations

Numerical methods for Poisson-Boltzmann equations

Fast algorithms for long-range interactions

Electromagnetic Scattering

Maxwell equations, potentials, and physical/artificial boundary conditions

Dyadic Green's functions in layered media

High order methods for surface electromagnetic integral equations

High order hierarchical Nedelec edge elements

Time domain methods - discontinuous Galerkin method and Yee scheme

Computing scattering in periodic structures and surface plasmons

Solving Schrödinger equations in waveguides and quantum dots

Electron Transport

Quantum electron transport in semiconductors

Non-equilibrium Green's function (NEGF) methods for transport

Numerical methods for Wigner quantum transport

Hydrodynamics electron transport and finite difference methods

Transport models in plasma media and numerical methods

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