Computational methods for electromagnetic phenomena : electrostatics in solvation, scattering, and electron transport / Wei Cai.

Includes bibliographical references and index.

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;
References;
Index.

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.