COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATIONPDF|Epub|txt|kindle电子书版本网盘下载

COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATIONPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Part Ⅰ Electrostatics in solvation1

1 Dielectric constant and fluctuation formulae for molecular dynamics3

1.1 Electrostatics of charges and dipoles3

1.2 Polarization P and displacement flux D5

1.2.1 Bound charges induced by polarization6

1.2.2 Electric field Epol（r） of a polarization density P（r）7

1.2.3 Singular integral expressions of Epol（r） inside dielectrics9

1.3 Clausius-Mossotti and Onsager formulae for dielectric constant9

1.3.1 Clausius-Mossotti formula for non-polar dielectrics9

1.3.2 Onsager dielectric theory for dipolar liquids11

1.4 Statistical molecular theory and dielectric fluctuation formulae16

1.4.1 Statistical methods for polarization density change ΔP18

1.4.2 Classical electrostatics for polarization density change ΔP20

1.4.3 Fluctuation formulae for dielectric constant e21

1.5 Appendices23

1.5.1 Appendix A： Average field of a charge in a dielectric sphere23

1.5.2 Appendix B： Electric field due to a uniformly polarized sphere24

1.6 Summary25

2 Poisson-Boltzmann electrostatics and analytical approximations26

2.1 Poisson-Boltzmann （PB） model for electrostatic solvation26

2.1.1 Debye-Hiickel Poisson-Boltzmann theory27

2.1.2 Helmholtz double layer and ion size effect30

2.1.3 Electrostatic solvation energy34

2.2 Generalized Born （GB） approximations of solvation energy36

2.2.1 Still’s generalized Born formulism37

2.2.2 Integral expression for Born radii37

2.2.3 FFT-based algorithm for the Born radii39

2.3 Method of images for reaction fields44

2.3.1 Methods of images for simple geometries45

2.3.2 Image methods for dielectric spheres47

2.3.3 Image methods for dielectric spheres in ionic solvent53

2.3.4 Image methods for multi-layered media55

2.4 Summary59

3 Numerical methods for Poisson-Boltzmann equations60

3.1 Boundary element methods （BEMs）60

3.1.1 Cauchy principal value （CPV） and Hadamard finite part（p.f.）61

3.1.2 Surface integral equations for the PB equations65

3.1.3 Computations of CPV and Hadamard p.f. and collocation BEMs71

3.2 Finite element methods （FEMs）82

3.3 Immersed interface methods （IIMs）85

3.4 Summary88

4 Fast algorithms for long-range interactions89

4.1 Ewald sums for charges and dipoles89

4.2 Particle-mesh Ewald （PME） methods96

4.3 Fast multipole methods for N-particle electrostatic interactions98

4.3.1 Multipole expansions98

4.3.2 A recursion for the local expansions （0 -→ L-level）102

4.3.3 A recursion for the multipole expansions （L→0-level）104

4.3.4 A pseudo-code for FMM104

4.3.5 Conversion operators for electrostatic FMM in R3105

4.4 Helmholtz FMM of wideband of frequencies for N-current source interactions107

4.5 Reaction field hybrid model for electrostatics110

4.6 Summary116

Part Ⅱ Electromagnetic scattering117

5 Maxwell equations， potentials， and physical/artificial boundary conditions119

5.1 Time-dependent Maxwell equations119

5.1.1 Magnetization M and magnetic field H120

5.2 Vector and scalar potentials122

5.2.1 Electric and magnetic potentials for time-harmonic fields123

5.3 Physical boundary conditions for E and H125

5.3.1 Interface conditions between dielectric media125

5.3.2 Leontovich impedance boundary conditions for conductors127

5.3.3 Sommerfeld and Silver-Müller radiation conditions129

5.4 Absorbing boundary conditions for E and H132

5.4.1 One-way wave Engquist-Majda boundary conditions132

5.4.2 High-order local non-reflecting Bayliss-Turkel conditions134

5.4.3 Uniaxial perfectly matched layer （UPML）138

5.5 Summary144

6 Dyadic Green’s functions in layered media145

6.1 Singular charge and current sources145

6.1.1 Singular charge sources145

6.1.2 Singular Hertz dipole current sources147

6.2 Dyadic Green’s functions GE（r│r’） and GH（r│r’）148

6.2.1 Dyadic Green’s functions for homogeneous media149

6.2.2 Dyadic Green’s functions for layered media150

6.2.3 Hankel transform for radially symmetric functions150

6.2.4 Transverse versus longitudinal field components152

6.2.5 Longitudinal components of Green’s functions153

6.3 Dyadic Green’s functions for vector potentials GA（r│r’）157

6.3.1 Sommerfeld potentials158

6.3.2 Transverse potentials160

6.4 Fast computation of dyadic Green’s functions160

6.5 Appendix： Explicit formulae165

6.5.1 Formulae for G1， G2， and G3， etc.165

6.5.2 Closed-form formulae for ψ（kρ）167

6.6 Summary169

7 High-order methods for surface electromagnetic integral equations170

7.1 Electric and magnetic field surface integral equations in layered media170

7.1.1 Integral representations170

7.1.2 Singular and hyper-singular surface integral equations175

7.2 Resonance and combined integral equations182

7.3 Nystr?m collocation methods for Maxwell equations185

7.3.1 Surface differential operators185

7.3.2 Locally corrected Nystr?m method for hyper-singular EFIE186

7.3.3 Nystr?m method for mixed potential EFIE190

7.4 Galerkin methods and high-order RWG current basis191

7.4.1 Galerkin method using vector-scalar potentials191

7.4.2 Functional space for surface current J（r）192

7.4.3 Basis functions over triangular-triangular patches194

7.4.4 Basis functions over triangular-quadrilateral patches198

7.5 Summary203

8 High-order hierarchical Nédélec edge elements205

8.1 Nédélec edge elements in H（curl）205

8.1.1 Finite element method for E or H wave equations206

8.1.2 Reference elements and Piola transformations208

8.1.3 Nédélec finite element basis in H（curl）209

8.2 Hierarchical Nédélec basis functions217

8.2.1 Construction on 2-D quadrilaterals218

8.2.2 Construction on 2-D triangles219

8.2.3 Construction on 3-D cubes222

8.2.4 Construction on 3-D tetrahedra223

8.3 Summary227

9 Time-domain methods - discontinuous Galerkin method and Yee scheme228

9.1 Weak formulation of Maxwell equations228

9.2 Discontinuous Galerkin （DG） discretization229

9.3 Numerical flux h（u-， u＋）230

9.4 Orthonormal hierarchical basis for DG methods234

9.4.1 Orthonormal hierarchical basis on quadrilaterals or hexahedra234

9.4.2 Orthonormal hierarchical basis on triangles or tetrahedra234

9.5 Explicit formulae of basis functions236

9.6 Computation of whispering gallery modes （WGMs） with DG methods238

9.6.1 WGMs in dielectric cylinders238

9.6.2 Optical energy transfer in coupled micro-cylinders239

9.7 Finite difference Yee scheme242

9.8 Summary245

10 Scattering in periodic structures and surface plasmons247

10.1 Bloch theory and band gap for periodic structures247

10.1.1 Bloch theory for 1-D periodic Helmholtz equations248

10.1.2 Bloch wave expansions250

10.1.3 Band gaps of photonic structures250

10.1.4 Plane wave method for band gap calculations252

10.1.5 Rayleigh-Bloch waves and band gaps by transmission spectra253

10.2 Finite element methods for periodic structures257

10.2.1 Nédélec edge element for eigen-mode problems257

10.2.2 Time-domain finite element methods for periodic array antennas261

10.3 Physics of surface plasmon waves265

10.3.1 Propagating plasmons on planar surfaces265

10.3.2 Localized surface plasmons268

10.4 Volume integral equation （VIE） for Maxwell equations270

10.5 Extraordinary optical transmission （EOT） in thin metallic films273

10.6 Discontinuous Galerkin method for resonant plasmon couplings274

10.7 Appendix： Auxiliary differential equation （ADE） DG methods for dispersive Maxwell equations276

10.7.1 Debye material277

10.7.2 Drude material282

10.8 Summary283

11 Schr?dinger equations for waveguides and quantum dots284

11.1 Generalized DG （GDG） methods for Schr?dinger equations284

11.1.1 One-dimensional Schr?dinger equations284

11.1.2 Two-dimensional Schr?dinger equations287

11.2 GDG beam propagation methods （BPMs） for optical waveguides289

11.2.1 Guided modes in optical waveguides289

11.2.2 Discontinuities in envelopes of guided modes294

11.2.3 GDG-BPM for electric fields296

11.2.4 GDG-BPM for magnetic fields299

11.2.5 Propagation of HE11 modes301

11.3 Volume integral equations for quantum dots302

11.3.1 One-particle Schr?dinger equation for electrons302

11.3.2 VIE for electrons in quantum dots304

11.3.3 Derivation of the VIE for quantum dots embedded in layered media306

11.4 Summary309

Part Ⅲ Electron transport311

12 Quantum electron transport in semiconductors313

12.1 Ensemble theory for quantum systems313

12.1.1 Thermal equilibrium of a quantum system313

12.1.2 Microcanonical ensembles315

12.1.3 Canonical ensembles316

12.1.4 Grand canonical ensembles319

12.1.5 Bose-Einstein and Fermi-Dirac distributions320

12.2 Density operator ρ for quantum systems324

12.2.1 One-particle density matrix ρ（x，x’）328

12.3 Wigner transport equations and Wigner-Moyal expansions329

12.4 Quantum wave transmission and Landauer current formula335

12.4.1 Transmission coefficient T（E）335

12.4.2 Current formula through barriers via T（E）337

12.5 Non-equilibrium Green’s function （NEGF） and transport current341

12.5.1 Quantum devices with one contact342

12.5.2 Quantum devices with two contacts346

12.5.3 Green’s function and transport current formula348

12.6 Summary348

13 Non-equilibrium Green’s function （NEGF） methods for transport349

13.1 NEGFs for 1-D devices349

13.1.1 1-D device boundary conditions for Green’s functions349

13.1.2 Finite difference methods for 1-D device NEGFs351

13.1.3 Finite element methods for 1-D device NEGFs353

13.2 NEGFs for 2-D devices354

13.2.1 2-D device boundary conditions for Green’s functions354

13.2.2 Finite difference methods for 2-D device NEGFs357

13.2.3 Finite element methods for 2-D device NEGFs359

13.3 NEGF simulation of a 29 nm double gate MOSFET361

13.4 Derivation of Green’s function in 2-D strip-shaped contacts363

13.5 Summary364

14 Numerical methods for Wigner quantum transport365

14.1 Wigner equations for quantum transport365

14.1.1 Truncation of phase spaces and charge conservation365

14.1.2 Frensley inflow boundary conditions367

14.2 Adaptive spectral element method （SEM）367

14.2.1 Cell averages in k-space368

14.2.2 Chebyshev collocation methods in x-space372

14.2.3 Time discretization372

14.2.4 Adaptive meshes for Wigner distributions374

14.3 Upwinding finite difference scheme375

14.3.1 Selections of Lcoh， Ncoh，Lk，and Nk375

14.3.2 Self-consistent algorithm through the Poisson equation376

14.3.3 Currents in RTD by NEGF and Wigner equations377

14.4 Calculation of oscillatory integrals On（z）378

14.5 Summary379

15 Hydrodynamic electron transport and finite difference methods380

15.1 Semi-classical and hydrodynamic models380

15.1.1 Semi-classical Boltzmann equations380

15.1.2 Hydrodynamic equations381

15.2 High-resolution finite difference methods of Godunov type388

15.3 Weighted essentially non-oscillatory （WENO） finite difference methods392

15.4 Central differencing schemes with staggered grids396

15.5 Summary400

16 Transport models in plasma media and numerical methods402

16.1 Kinetic and macroscopic magneto-hydrodynamic （MHD） theories402

16.1.1 Vlasov-Fokker-Planck equations402

16.1.2 MHD equations for plasma as a conducting fluid404

16.2 Vlasov-Fokker-Planck （VFP） schemes410

16.3 Particle-in-cell （PIC） schemes413

16.4 ？·B＝0 constrained transport methods for MHD equations414

16.5 Summary418

References419

Index441