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

Table of Contents:
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.

About the Author :
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.

Review :
'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 'This book is a great and unique contribution to computational modeling of electromagnetic problems across many fields, covering in depth all interesting multiscale phenomena, from electrostatics in biomolecules, to EM scattering, to electron transport in plasmas, and quantum electron transport in semiconductors. It includes both atomistic descriptions and continuum based formulations with emphasis on long-range interactions and high-order algorithms, respectively. The book is divided into three main parts and includes both established but also new algorithms on every topic addressed, e.g. fast multipole expansions, boundary integral equations, high-order finite elements, discontinuous Galerkin and WENO methods. Both the organization of the material and the exposition of physical and algorithmic concepts are superb and make the book accessible to researchers and students in every discipline.' George Karniadakis, Professor of Applied Mathematics, Brown University 'This is an excellent book for one who wants to study and understand the relationship between mathematical methods and the many different physical problems they can model and solve.' Weng Cho Chew, Y. T. Lo Chair Professor in Electrical and Computer Engineering, University of Illinois, Urbana-Champaign 'A well-written book which will be of use to a broad range of students and researchers in applied mathematics, applied physics and engineering. It provides a clear presentation of many topics in computational electromagnetics and illustrates their importance in a distinctive and diverse set of applications.' Leslie Greengard, Courant Institute, New York University