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Mutable αr in magnetic models #159

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315 changes: 161 additions & 154 deletions src/PhysicalModels/MagneticModels.jl
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# ===================


function Base.getproperty(obj::Magneto, prop::Symbol)
if prop === :αr
return getfield(obj, :αr)[] # Return the value of the internal reference
else
return getfield(obj, prop) # Fallback to the default implementation
end
end


function Base.setproperty!(obj::Magneto, prop::Symbol, val)
if prop === :αr
return getfield(obj, :αr)[] = val # Set the value to the internal reference
else
return setfield!(obj, prop, val) # Constitutive models are inmutable: this statement will throw the default error.
end
end


struct Magnetic <: Magneto
μ::Float64
αr::Ref{Float64}
χe::Float64

function Magnetic(; μ0::Float64, αr::Float64, χe::Float64=0.0)
new(μ0, Ref(αr), χe)
χe::Float64
Magnetic(; μ0::Float64, αr::Float64, χe::Float64=0.0) = new(μ0, Ref(αr), χe)
end

function (obj::Magnetic)(Λ::Float64=1.0)
μ, αr, χe = obj.μ, obj.αr, obj.χe
ℋᵣ(N) = αr[] * Λ * N
# Energy #
(; μ, χe) = obj # αr is a reference. Accessing it will dereference the internal value.
ℋᵣ(N) = obj.αr * Λ * N
Ψmm(ℋ₀, N) = (-μ / 2.0) * ((ℋ₀ + ℋᵣ(N)) ⋅ (ℋ₀ + ℋᵣ(N))) * (1 + χe)
∂Ψmm_∂φ(ℋ₀, N) = (-μ) * (ℋ₀ + ℋᵣ(N)) * (1 + χe)
∂Ψmm_∂φφ(ℋ₀, N) = (-μ) * Id(N) * (1 + χe)
return (Ψmm, ∂Ψmm_∂φ, ∂Ψmm_∂φφ)
end


end


struct IdealMagnetic <: Magneto
μ::Float64
χe::Float64
function IdealMagnetic(; μ0::Float64, χe::Float64=0.0)
new(μ0, χe)
end
function (obj::IdealMagnetic)(Λ::Float64=1.0)

μ, χe = obj.μ, obj.χe
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = ∂Ψmm_∂H(F, ℋ₀) × F + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I3 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = (F × (∂Ψmm_∂HH(F, ℋ₀) × F)) +
H(F) ⊗₁₂³⁴ (∂Ψmm_∂HJ(F, ℋ₀) × F) +
(∂Ψmm_∂HJ(F, ℋ₀) × F) ⊗₁₂³⁴ H(F) +
∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗₁₂³⁴ H(F)) +
×ᵢ⁴(∂Ψmm_∂H(F, ℋ₀) + ∂Ψmm_∂J(F, ℋ₀) * F)

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I3 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)

∂Ψmm_∂φu(F, ℋ₀) = (∂Ψmm_∂ℋ₀H(F, ℋ₀) × F) + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)

return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end
IdealMagnetic(; μ0::Float64, χe::Float64=0.0) = new(μ0, χe)
end

function (obj::IdealMagnetic)(Λ::Float64=1.0)
(; μ, χe) = obj
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = ∂Ψmm_∂H(F, ℋ₀) × F + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I3 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = (F × (∂Ψmm_∂HH(F, ℋ₀) × F)) +
H(F) ⊗₁₂³⁴ (∂Ψmm_∂HJ(F, ℋ₀) × F) +
(∂Ψmm_∂HJ(F, ℋ₀) × F) ⊗₁₂³⁴ H(F) +
∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗₁₂³⁴ H(F)) +
×ᵢ⁴(∂Ψmm_∂H(F, ℋ₀) + ∂Ψmm_∂J(F, ℋ₀) * F)

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I3 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)

∂Ψmm_∂φu(F, ℋ₀) = (∂Ψmm_∂ℋ₀H(F, ℋ₀) × F) + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)

return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end


struct IdealMagnetic2D <: Magneto
μ::Float64
χe::Float64
function IdealMagnetic2D(; μ0::Float64, χe::Float64=0.0)
new(μ0, χe)
end
IdealMagnetic2D(; μ0::Float64, χe::Float64=0.0) = new(μ0, χe)
end

function (obj::IdealMagnetic2D)(Λ::Float64=1.0)

μ, χe = obj.μ, obj.χe
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = (tr(∂Ψmm_∂H(F, ℋ₀)) * I2) - ∂Ψmm_∂H(F, ℋ₀)' + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I2 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = _∂H∂F_2D()' * ∂Ψmm_∂HH(F, ℋ₀) * _∂H∂F_2D() + _∂H∂F_2D()' * (∂Ψmm_∂HJ(F, ℋ₀) ⊗ H(F)) +
(H(F) ⊗ ∂Ψmm_∂HJ(F, ℋ₀)) * _∂H∂F_2D() + ∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗ H(F)) + ∂Ψmm_∂J(F, ℋ₀) * _∂H∂F_2D()

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I2 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂φu(F, ℋ₀) = ∂Ψmm_∂ℋ₀H(F, ℋ₀) * _∂H∂F_2D() + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end
function (obj::IdealMagnetic2D)(Λ::Float64=1.0)
(; μ, χe) = obj
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = (tr(∂Ψmm_∂H(F, ℋ₀)) * I2) - ∂Ψmm_∂H(F, ℋ₀)' + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I2 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = _∂H∂F_2D()' * ∂Ψmm_∂HH(F, ℋ₀) * _∂H∂F_2D() + _∂H∂F_2D()' * (∂Ψmm_∂HJ(F, ℋ₀) ⊗ H(F)) +
(H(F) ⊗ ∂Ψmm_∂HJ(F, ℋ₀)) * _∂H∂F_2D() + ∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗ H(F)) + ∂Ψmm_∂J(F, ℋ₀) * _∂H∂F_2D()

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I2 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂φu(F, ℋ₀) = ∂Ψmm_∂ℋ₀H(F, ℋ₀) * _∂H∂F_2D() + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end


struct HardMagnetic <: Magneto
μ::Float64
αr::Float64
αr::Ref{Float64}
χe::Float64
χr::Float64
χt::Float64
βmok::Float64
βcoup::Float64
function HardMagnetic(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, χt::Union{Float64,Nothing}=nothing, βmok::Float64=0.0, βcoup::Float64=0.0)
χt_val = isnothing(χt) ? χe : χt
new(μ0, αr, χe, χr, χt_val, βmok, βcoup)
χt = isnothing(χt) ? χe : χt
new(μ0, Ref(αr), χe, χr, χt, βmok, βcoup)
end
end

function (obj::HardMagnetic)(Λ::Float64=1.0)
μ, χe = obj.μ, obj.χe
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = ∂Ψmm_∂H(F, ℋ₀) × F + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I3 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = (F × (∂Ψmm_∂HH(F, ℋ₀) × F)) +
H(F) ⊗₁₂³⁴ (∂Ψmm_∂HJ(F, ℋ₀) × F) +
(∂Ψmm_∂HJ(F, ℋ₀) × F) ⊗₁₂³⁴ H(F) +
∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗₁₂³⁴ H(F)) +
×ᵢ⁴(∂Ψmm_∂H(F, ℋ₀) + ∂Ψmm_∂J(F, ℋ₀) * F)

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I3 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)

∂Ψmm_∂φu(F, ℋ₀) = (∂Ψmm_∂ℋ₀H(F, ℋ₀) × F) + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end
function (obj::HardMagnetic)(Λ::Float64=1.0)
(; μ, χe) = obj
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = ∂Ψmm_∂H(F, ℋ₀) × F + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I3 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = (F × (∂Ψmm_∂HH(F, ℋ₀) × F)) +
H(F) ⊗₁₂³⁴ (∂Ψmm_∂HJ(F, ℋ₀) × F) +
(∂Ψmm_∂HJ(F, ℋ₀) × F) ⊗₁₂³⁴ H(F) +
∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗₁₂³⁴ H(F)) +
×ᵢ⁴(∂Ψmm_∂H(F, ℋ₀) + ∂Ψmm_∂J(F, ℋ₀) * F)

∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I3 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)

∂Ψmm_∂φu(F, ℋ₀) = (∂Ψmm_∂ℋ₀H(F, ℋ₀) × F) + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end


Expand All @@ -171,40 +179,39 @@ struct HardMagnetic2D <: Magneto
βmok::Float64
βcoup::Float64
function HardMagnetic2D(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, χt::Union{Float64,Nothing}=nothing, βmok::Float64=0.0, βcoup::Float64=0.0)
χt_val = isnothing(χt) ? χe : χt
new(μ0, Ref(αr), χe, χr, χt_val, βmok, βcoup)
χt = isnothing(χt) ? χe : χt
new(μ0, Ref(αr), χe, χr, χt, βmok, βcoup)
end
end

function (obj::HardMagnetic2D)(Λ::Float64=1.0)

μ, χe = obj.μ, obj.χe
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = (tr(∂Ψmm_∂H(F, ℋ₀)) * I2) - ∂Ψmm_∂H(F, ℋ₀)' + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I2 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = _∂H∂F_2D()' * ∂Ψmm_∂HH(F, ℋ₀) * _∂H∂F_2D() + _∂H∂F_2D()' * (∂Ψmm_∂HJ(F, ℋ₀) ⊗ H(F)) +
(H(F) ⊗ ∂Ψmm_∂HJ(F, ℋ₀)) * _∂H∂F_2D() + ∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗ H(F)) + ∂Ψmm_∂J(F, ℋ₀) * _∂H∂F_2D()


∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I2 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂φu(F, ℋ₀) = ∂Ψmm_∂ℋ₀H(F, ℋ₀) * _∂H∂F_2D() + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end
function (obj::HardMagnetic2D)(Λ::Float64=1.0)
(; μ, χe) = obj
J(F) = det(F)
H(F) = J(F) * inv(F)'

# Energy #
Hℋ₀(F, ℋ₀) = H(F) * ℋ₀
Hℋ₀Hℋ₀(F, ℋ₀) = Hℋ₀(F, ℋ₀) ⋅ Hℋ₀(F, ℋ₀)
Ψmm(F, ℋ₀) = (-μ / (2.0 * J(F))) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)

# First Derivatives #
∂Ψmm_∂H(F, ℋ₀) = (-μ / (J(F))) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂J(F, ℋ₀) = (+μ / (2.0 * J(F)^2.0)) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂ℋ₀(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂u(F, ℋ₀) = (tr(∂Ψmm_∂H(F, ℋ₀)) * I2) - ∂Ψmm_∂H(F, ℋ₀)' + ∂Ψmm_∂J(F, ℋ₀) * H(F)
∂Ψmm_∂φ(F, ℋ₀) = ∂Ψmm_∂ℋ₀(F, ℋ₀)

# Second Derivatives #
∂Ψmm_∂HH(F, ℋ₀) = (-μ / (J(F))) * (I2 ⊗₁₃²⁴ (ℋ₀ ⊗ ℋ₀)) * (1 + χe)
∂Ψmm_∂HJ(F, ℋ₀) = (+μ / (J(F))^2.0) * (Hℋ₀(F, ℋ₀) ⊗ ℋ₀) * (1 + χe)
∂Ψmm_∂JJ(F, ℋ₀) = (-μ / (J(F))^3.0) * Hℋ₀Hℋ₀(F, ℋ₀) * (1 + χe)
∂Ψmm_∂uu(F, ℋ₀) = _∂H∂F_2D()' * ∂Ψmm_∂HH(F, ℋ₀) * _∂H∂F_2D() + _∂H∂F_2D()' * (∂Ψmm_∂HJ(F, ℋ₀) ⊗ H(F)) +
(H(F) ⊗ ∂Ψmm_∂HJ(F, ℋ₀)) * _∂H∂F_2D() + ∂Ψmm_∂JJ(F, ℋ₀) * (H(F) ⊗ H(F)) + ∂Ψmm_∂J(F, ℋ₀) * _∂H∂F_2D()


∂Ψmm_∂ℋ₀H(F, ℋ₀) = (-μ / (J(F))) * ((I2 ⊗₁₃² Hℋ₀(F, ℋ₀)) + (H(F)' ⊗₁₂³ ℋ₀)) * (1 + χe)
∂Ψmm_∂ℋ₀J(F, ℋ₀) = (+μ / (J(F))^2.0) * (H(F)' * Hℋ₀(F, ℋ₀)) * (1 + χe)
∂Ψmm_∂φu(F, ℋ₀) = ∂Ψmm_∂ℋ₀H(F, ℋ₀) * _∂H∂F_2D() + (∂Ψmm_∂ℋ₀J(F, ℋ₀) ⊗₁²³ H(F))
∂Ψmm_∂φφ(F, ℋ₀) = (-μ / (J(F))) * (H(F)' * H(F)) * (1 + χe)
return (Ψmm, ∂Ψmm_∂u, ∂Ψmm_∂φ, ∂Ψmm_∂uu, ∂Ψmm_∂φu, ∂Ψmm_∂φφ)
end
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