Computational Methods for Electromagnetic Phenomena

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, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: • Statistical fluctuation formulae 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 Greens function) and Wigner kinetic methods for quantum transport • High-order WENO and Godunov and central schemes for hydrodynamic transport • Vlasov-Fokker-Planck and PIC and constrained MHD transport in plasmas

Part I. Electrostatics in Solvations:
1. Dielectric constant and fluctuation formulae for molecular dynamics
2. Poisson–Boltzmann electrostatics and analytical approximations
3. Numerical methods for Poisson–Boltzmann equations
4. Fast algorithms for long-range interactions
Part II. Electromagnetic Scattering:
5. Maxwell equations, potentials, and physical/artificial boundary conditions
6. Dyadic Green's functions in layered media
7. High order methods for surface electromagnetic integral equations
8. High order hierarchical Nedelec edge elements
9. Time domain methods – discontinuous Galerkin method and Yee scheme
10. Computing scattering in periodic structures and surface plasmons
11. Solving Schrödinger equations in waveguides and quantum dots
Part III. Electron Transport:
12. Quantum electron transport in semiconductors
13. Non-equilibrium Green's function (NEGF) methods for transport
14. Numerical methods for Wigner quantum transport
15. Hydrodynamics electron transport and finite difference methods
16. Transport models in plasma media and numerical methods.