Computational Methods for Electromagnetic Phenomena: by Wei Cai

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By Wei Cai

A different and accomplished graduate textual content and reference on numerical tools for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state of the art numerical tools defined comprise:

• Statistical fluctuation formulae for the dielectric constant

• Particle-Mesh-Ewald, Fast-Multipole-Method and image-based response box strategy for long-range interactions

• High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and quantity quintessential equipment in layered media for Poisson-Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots

• soaking up and UPML boundary stipulations

• High-order hierarchical Nédélec part components

• High-order discontinuous Galerkin (DG) and Yee finite distinction time-domain equipment

• Finite aspect and airplane wave frequency-domain equipment for periodic buildings

• Generalized DG beam propagation procedure for optical waveguides

• NEGF(Non-equilibrium Green's functionality) and Wigner kinetic equipment for quantum transport

• High-order WENO and Godunov and critical schemes for hydrodynamic delivery

• Vlasov-Fokker-Planck and PIC and restricted MHD shipping in plasmas

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

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81) N k=−N/2 where ξk = k(2πΩ/N ) and N will be selected based on the Shannon sampling rate of T = π/L (Shannon & Weaver, 1963; Daubechies, 1992) for a plane wave eiξL of wave number L in the ξ variable: 2πΩ = 2ΩL. 82) T In principle, the selection of N should also depend on the oscillatory behavior ˆ of the spectral functions fˆ(ξ) and G(ξ). In the case that a larger N is needed to ˆ resolve the oscillations in fˆ(ξ) and G(ξ), we can achieve that by increasing the size of L. N= Calculation of Φ(xj ), xj = j(2L/N ) ∈ [−L, L], −N/2 ≤ j ≤ N/2 − 1 Next, we calculate the value of Φ(xj ) at N points inside the interval [−L, L].

78) • Local field Elocal The local field acting on a molecule with a permanent dipole moment will now consist of two parts: the reaction field from the permanent dipole μ and the directing field Ed . Namely, we have Elocal = Ed + Erf . 62): Erf = f f μ2 μ= Ed . 80) that Elocal = = μ2 f 1 − f α 3kB T μ2 f 1+ 1 − f α 3kB T 1+ Ed 1 3 r E. 4 1 1 2( 4π 0 R3 2 r r − 1) . +1 Statistical molecular theory and dielectric fluctuation formulae In this section we will derive fluctuation formulae for computing dielectric constants using dipole moment fluctuations obtained through molecular dynamics simulations of dipolar liquids, which allow realistic modeling of the material systems.

13) is unknown due to the nonlinearity of the equation and the complex geometric 36 PB electrostatics and analytical approximations shape of the solute biomolecule. Approximate solutions are given later in this chapter. 49) where qi n0i exp − S(φ) = − i qi φ kB T . 16) where S becomes a linear function, can be further simplified to Wed = 1 2 drρ(r)Φ(r). 47) for the linearized PB model except for the included additional self-energy term from the Coulomb potential generated by the density ρ(r) in the reference environment, usually taken to be the vacuum.

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