NESSie.Radon

_regularyukawapot(
          ::Type{SingleLayer},
    x     ::AbstractVector{T},
    ξ     ::AbstractVector{T},
    yukawa::T,
          ::AbstractVector{T}=T[]
)

Computes the regular part of the Yukawa potential, that is, Yukawa minus Laplace:

\[\mathcal{G}^Y-\mathcal{G}^L = \frac{1}{4π}\frac{e^{-\frac{|x - ξ|}{Λ}} - 1}{|x-ξ|}\]

Arguments

• yukawa Exponent of the Yukawa operator's fundamental solution

Return type

T

_regularyukawapot(
          ::Type{DoubleLayer},
    x     ::AbstractVector{T},
    ξ     ::AbstractVector{T},
    yukawa::T,
    normal::AbstractVector{T}
)

Computes the normal derivative of the regular part of the Yukawa potential, that is, Yukawa minus Laplace:

\[\frac{∂}{∂n} \frac{1}{4π} \frac{e^{-\frac{|x - ξ|}{Λ}} - 1}{|x-ξ|} = \frac{1}{4π} \frac{1 - (1 + Λ^{-1} |x - ξ|)e^{-\frac{|x - ξ|}{Λ}}}{|x-ξ|²} \frac{(x - ξ) ⋅ n}{|x - ξ|}\]

Arguments

• yukawa Exponent of the Yukawa operator's fundamental solution

Return type

T