NESSie.Radon
NESSie.Radon._regularyukawapot
— Function_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