Computational Methods for Electromagnetic Phenomena

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.

'This is a truly unique book that covers a variety of computational methods for several important physical (electromagnetics) problems in a rigorous manner with a great depth. It will benefit not only computational mathematicians, but also physicists and electrical engineers interested in numerical analysis of electrostatic, electrodynamic, and electron transport problems. The breadth (both in terms of physics and numerical analysis) and depth are very impressive. I like, in particular, the way the book is organized: a physical problem is described clearly first and then followed by the presentation of relevant state-of-the-art computational methods.' Jian-Ming Jin, Y. T. Lo Chair Professor in Electrical and Computer Engineering, University of Illinois, Urbana-Champaign

• 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.