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

ISBN-13: 9781107021051 / Angielski / Twarda / 2013 / 461 str.

Wei Cai

Opis

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 (Nystrom 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 Nedelec 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
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Recenzje

'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

Spis treści

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.