NESSie.BEM

_get_laplace_matrices(
    Ξ       ::Vector{Vector{T}},
    elements::Vector{Triangle{T}}
)

Constructs and returns implicit representations for the single- and double-layer Laplace potential matrices V and K for the given observation points and surface elements.

Return type

[Tuple{InteractionMatrix{T}, InteractionMatrix{T}}] (https://tkemmer.github.io/ImplicitArrays.jl/stable/#ImplicitArrays.InteractionMatrix)

_get_yukawa_matrices(
    Ξ       ::Vector{Vector{T}},
    elements::Vector{Triangle{T}},
    yuk     ::T
)

Constructs and returns implicit representations for the single- and double-layer Yukawa potential matrices V^Y and K^Y for the given observation points and surface elements.

Return type

[Tuple{InteractionMatrix{T}, InteractionMatrix{T}}] (https://tkemmer.github.io/ImplicitArrays.jl/stable/#ImplicitArrays.InteractionMatrix)

_solve_explicit(
         ::Type{<: LocalityType},
    model::Model{T, Triangle{T}}
)

Computes the full local or nonlocal cauchy data on the surface of the biomolecule using an explicit representation of the BEM system.

Return type

LocalBEMResult{T, Triangle{T}} or NonlocalBEMResult{T, Triangle{T}}

_solve_implicit(
         ::Type{<: LocalityType},
    model::Model{T, Triangle{T}}
)

Computes the full local or nonlocal cauchy data on the surface of the biomolecule using an implicit representation of the BEM system.

Return type

LocalBEMResult{T, Triangle{T}} or NonlocalBEMResult{T, Triangle{T}}

_solve_linear_system(
    A::AbstractArray{T, 2},
    b::AbstractArray{T, 1}
)

Solves the linear system Ax = b from A and b using a Jacobi-preconditioned GMRES solver.

Return type

Array{T, 1}

Supported keyword arguments

Everything from [IterativeSolvers.gmres] (https://iterativesolvers.julialinearalgebra.org/stable/linear_systems/gmres/) except for log.

struct Kfun{T} <: InteractionFunction{Vector{T}, Triangle{T}, T} end

Interaction function for an implicit representation of potential matrix K.

struct Kyfun{T} <: InteractionFunction{Vector{T}, Triangle{T}, T}
    yuk::T   # exponent of the Yukawa operator's fundamental solution
end

Interaction function for an implicit representation of potential matrix Kʸ.

struct Vfun{T} <: InteractionFunction{Vector{T}, Triangle{T}, T} end

Interaction function for an implicit representation of potential matrix V.

struct Vyfun{T} <: InteractionFunction{Vector{T}, Triangle{T}, T}
    yuk::T   # exponent of the Yukawa operator's fundamental solution
end

Interaction function for an implicit representation of potential matrix Vʸ.

struct LocalSystemMatrix{T} <: AbstractArray{T, 2}
    K     ::InteractionMatrix{T}   # double-layer Laplace
    params::Option{T}              # System constants
end

Implicit representation of the first local BEM system matrix.

struct NonlocalSystemMatrix{T} <: AbstractArray{T, 2}
    V     ::InteractionMatrix{T}   # single-layer Laplace
    K     ::InteractionMatrix{T}   # double-layer Laplace
    Vy    ::InteractionMatrix{T}   # single-layer Yukawa
    Ky    ::InteractionMatrix{T}   # double-layer Yukawa
    params::Option{T}              # system constants
end

Implicit representation of the nonlocal BEM system matrix.

Special constructors

function NonlocalSystemMatrix{T}(
    Ξ       ::Vector{Vector{T}},
    elements::Vector{Triangle{T}},
    params  ::Option{T}
) where T

Creates the nonlocal system matrix directly from the given observation points Ξ and surface elements.

_espotential_Γ(ξ::Vector{T}, bem::BEMResult{T})
_espotential_Γ(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal electrostatic potential for (an) observation point(s) ξ (Ξ) on the molecular surface.

Supported keyword arguments

See molpotential

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}

_espotential_Ω(ξ::Vector{T}, bem::BEMResult{T})
_espotential_Ω(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal electrostatic potential for (an) observation point(s) ξ (Ξ) inside the molecule.

Supported keyword arguments

See molpotential

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}

_espotential_Σ(ξ::Vector{T}, bem::BEMResult{T})
_espotential_Σ(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal electrostatic potential for (an) observation point(s) ξ (Ξ) in the solvent domain.

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}

_rfpotential_Γ(ξ::Vector{T}, bem::BEMResult{T})
_rfpotential_Γ(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal reaction field potential for (an) observation point(s) ξ (Ξ) on the molecular surface.

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}

_rfpotential_Ω(ξ::Vector{T}, bem::BEMResult{T})
_rfpotential_Ω(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal reaction field potential for (an) observation point(s) ξ (Ξ) inside the molecule.

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}

_rfpotential_Σ(ξ::Vector{T}, bem::BEMResult{T})
_rfpotential_Σ(Ξ::AbstractVector{Vector{T}}, bem::BEMResult{T})

Computes the local or nonlocal reaction field potential for (an) observation point(s) ξ (Ξ) in the solvent domain.

Supported keyword arguments

See molpotential

Unit

$V = \frac{C}{F}$

Return type

T or Vector{T}