Computational Methods for Electromagnetic Phenomena Electrostatics in Solvation, Scattering, and Electron Transport

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 Green's 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.

The first book of its kind to cover a wide range of computational methods for electromagnetic phenomena, from atomistic to continuum scales, this integrated and balanced treatment of mathematical formulations, algorithms and the underlying physics enables us to engage in innovative, advanced interdisciplinary computational research.

Wei Cai has been a full professor at the University of North Carolina since 1999. He has also taught and conducted research at the University of California, Santa Barbara, Peking University, Fudan University and Shanghai Jiaotong University. He has published over 80 referred journal articles and was awarded the prestigious Feng Kang prize in scientific computing in 2005.