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

Wei Cai is currently the Clements Chair of Applied Mathematics at Southern Methodist University and has published over 120 referred journal articles and was awarded the prestigious Feng Kang prize in scientific computing in 2005.