Models

abstract type Element{T <: AbstractFloat} end
abstract type SurfaceElement{T} <: Element{T} end
abstract type VolumeElement{T}  <: Element{T} end

Abstract base types for all elements.

struct Triangle{T} <: SurfaceElement{T}
    v1      ::Vector{T}   # position of the first node
    v2      ::Vector{T}   # position of the second node
    v3      ::Vector{T}   # position of the third node
    center  ::Vector{T}   # centroid of the triangle
    normal  ::Vector{T}   # normal vector of the triangle
    area    ::T           # area of the triangle
    distorig::T           # distance to the origin
end

Representation of a single surface triangle.

Special constructors

Triangle(
    v1  ::Vector{T},
    v2  ::Vector{T},
    v3  ::Vector{T}
)

Most commonly used constructor variant for creating a triangle by only specifying its nodes. The remaining member variables will automatically be computed via props.

struct Tetrahedron{T} <: VolumeElement{T}
    v1::Vector{T}       # position of the first node
    v2::Vector{T}       # position of the second node
    v3::Vector{T}       # position of the third node
    v4::Vector{T}       # position of the fourth node
    domain::Symbol      # element domain (solvent :Σ, solute :Ω, or :none)
end

Representation of a single tetrahedron.

Special constructors

Tetrahedron(
    v1::Vector{T},
    v2::Vector{T},
    v3::Vector{T},
    v4::Vector{T}
)

Sets domain to :none.

struct Charge{T <: AbstractFloat}
    pos::Vector{T}  # position of the charge
    val::T          # charge value
end

Representation of a single point charge.

Special constructors

Charge(
    posx::T,
    posy::T,
    posz::T,
    val ::T
)

Constructor variant with flat argument list for pos.

mutable struct Model{T, E <: Element{T}}
    nodes   ::Vector{Vector{T}  = Vector{T}[]    # mesh nodes
    elements::Vector{E}         = E[]            # mesh elements
    charges ::Vector{Charge{T}} = Charge{T}[]    # point charges in the molecule
    params  ::Option{T}         = defaultopt(T)  # system constants
end

System model representing a biomelecule in solvation, including a collection of point charges in the molecule and a set of system constants. The system can either be represented as a surface model (e.g., a collection of molecule surface triangles) or as a volume model (e.g., a collection of tetrahedra for the molecule and its surrounding space).

struct BornIon{T <: AbstractFloat}
    charge::Charge{T}  # point charge at the sphere's center
    radius::T          # sphere radius in Å
end

Single Born ion, that is, a monoatomic ion represented as a spherically symmetric domain with a single point charge located at its center ($ε_Ω = 1$).

Special constructors

BornIon(charge::T, radius::T)

Centers the sphere at $(0, 0, 0)^T$.

bornion(name::String, ::Type{Float64} = Float64)
bornion(name::String, ::Type{Float32})

Generator function for built-in Born ions:

Return type

BornIon

mutable struct XieModel{T}
    radius ::T                                 # radius of the origin-centered sphere
    charges::Vector{Charge{T}}                 # point charges in the sphere
    params ::Option{T}         = defaultopt(T) # system constants
end

System model of a dielectric sphere containing multiple point charges. On construction, the given point charge model will be translated and rescaled to fit inside an origin-centered sphere with the specified radius.

Special contructors

XieModel(
    radius ::T,
    charges::Vector{Charge{T}},
    params ::Option{T}          = defaultopt(T);
    # kwargs
    compat ::Bool               = false
)

compat enables the compatibility mode and scales the model exactly like the reference implementation ([Xie16]). Use this flag if you intend to compare the results to the reference.

struct NonlocalXieModel1{T}
    radius ::T                 # radius of the origin-centered sphere
    charges::Vector{Charge{T}} # point charges in the sphere
    params ::Option{T}         # system constants
    len    ::Int               # number of terms to be computed
    A₁     ::Array{T, 2}       # coefficients A₁ for each charge
    A₂     ::Array{T, 2}       # coefficients A₂ for each charge
    A₃     ::Array{T, 2}       # coefficients A₃ for each charge
end

Representation of the first nonlocal Poisson dielectric model described in [Xie16]. This model comprises a full XieModel and the coefficients $A_{in}$ with $i = 1, 2, 3$ (cf. Eqs. (20a-c)) for each point charge in the model, which are used in the computation of the electrostatic potentials.

Constructor

NonlocalXieModel1(
    model::XieModel{T},
    len  ::Int
)

The model is created solely from the given XieModel and the number of terms to be used to approximate the original infinite sum (Eq. 18). The coefficient vectors are computed automatically via coefficients.