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COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATIONPDF电子书下载

其他书籍

• 作 者：SCATTERING
• 出 版 社：CAMBRIDGE UNIVERSITY PRESS
• 出版年份：2013
• ISBN：
• 页数：444 页

图书介绍： 查看图书目录点击购买PDF全本电子书 上一篇：ADVANCED MECHANICS OF MATERIALS FIFTH EDITION下一篇：Experiments in General 《COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATION》目录 标签：

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

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• 3易经真的很容易
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摘要：本文以“COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATION.pdf电子书版文档下载”为中心，详细阐述了该文档在电磁现象静电学领域的计算方法。全文分为四个部分，分别从计算方法概述、数值模拟技术、软件应用及发展趋势等方面进行深入探讨，旨在为电磁现象静电学领域的研究提供有益的参考。

1、计算方法概述

计算方法在电磁现象静电学领域扮演着至关重要的角色。本文首先对计算方法进行了概述，包括有限元法、边界元法、积分方程法等。这些方法在处理复杂电磁场问题时具有显著优势，能够有效提高计算精度和效率。

有限元法是一种基于变分原理的数值方法，通过将求解区域划分为有限个单元，将连续问题离散化，从而求解电磁场问题。边界元法则是通过求解边界上的积分方程来求解电磁场问题，具有计算效率高、精度好的特点。积分方程法则是通过求解积分方程来求解电磁场问题，适用于复杂边界和介质。

此外，计算方法在电磁现象静电学领域的应用还包括时域有限差分法、频域有限差分法等。这些方法在处理电磁场问题时具有不同的特点和适用范围，为电磁现象静电学领域的研究提供了丰富的计算手段。

2、数值模拟技术

数值模拟技术在电磁现象静电学领域具有广泛的应用。本文从以下几个方面对数值模拟技术进行了阐述。

首先，数值模拟技术可以用于电磁场问题的数值求解。通过将电磁场问题离散化，将连续问题转化为离散问题，从而求解电磁场问题。其次，数值模拟技术可以用于电磁场问题的可视化。通过将电磁场数据可视化，可以直观地了解电磁场分布和特性。最后，数值模拟技术可以用于电磁场问题的优化设计。通过模拟电磁场在不同参数下的变化，可以优化电磁场设计，提高电磁场性能。

此外，数值模拟技术在电磁现象静电学领域的应用还包括电磁兼容性分析、电磁场防护设计等。通过数值模拟技术，可以预测电磁场对电子设备的影响，为电磁兼容性设计提供依据。

3、软件应用

软件在电磁现象静电学领域具有重要作用。本文从以下几个方面对软件应用进行了阐述。

首先，软件可以用于电磁场问题的数值求解。如ANSYS、COMSOL等软件，具有强大的数值求解功能，能够处理复杂的电磁场问题。其次，软件可以用于电磁场问题的可视化。如MATLAB、Python等软件，具有丰富的可视化工具，可以直观地展示电磁场分布和特性。最后，软件可以用于电磁场问题的优化设计。如OptiStruct、ANSYS DesignXplorer等软件，可以优化电磁场设计，提高电磁场性能。

此外，软件在电磁现象静电学领域的应用还包括电磁场仿真、电磁场测试等。通过软件，可以模拟电磁场在不同参数下的变化，为电磁场设计提供依据。

4、发展趋势

随着科学技术的不断发展，电磁现象静电学领域的计算方法、数值模拟技术和软件应用正朝着以下方向发展。

首先，计算方法将更加高效、精确。随着计算技术的发展，计算方法将不断优化，提高计算精度和效率。其次，数值模拟技术将更加智能化。通过引入人工智能、大数据等技术，数值模拟技术将实现智能化，提高电磁场问题的求解能力。最后，软件应用将更加普及。随着软件技术的不断发展，软件应用将更加普及，为电磁现象静电学领域的研究提供更加便捷的工具。

总结：

本文对“COMPUTATIONAL METHODS FOR ELECTROMAGNETIC PHENOMENA ELECTROSTATICS IN SOLVATION.pdf电子书版文档下载”进行了详细阐述，从计算方法概述、数值模拟技术、软件应用及发展趋势等方面进行了深入探讨。这些内容为电磁现象静电学领域的研究提供了有益的参考。

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