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add depolarization field due to metal electrode to total energy density #45

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add depolarization field due to metal electrode to total energy density #45

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13 changes: 13 additions & 0 deletions Source/FerroX.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -184,6 +184,9 @@ AMREX_GPU_MANAGED amrex::Real FerroX::epsilonX_fe_tphase;
AMREX_GPU_MANAGED amrex::Real FerroX::epsilonZ_fe;
AMREX_GPU_MANAGED amrex::Real FerroX::epsilon_de;
AMREX_GPU_MANAGED amrex::Real FerroX::epsilon_si;
AMREX_GPU_MANAGED amrex::Real FerroX::epsilon_metal;
AMREX_GPU_MANAGED amrex::Real FerroX::metal_screening_length;
AMREX_GPU_MANAGED amrex::Real FerroX::metal_thickness;
AMREX_GPU_MANAGED amrex::Real FerroX::alpha; // alpha = 2*alpha_1
AMREX_GPU_MANAGED amrex::Real FerroX::beta; // beta = 4*alpha_11
AMREX_GPU_MANAGED amrex::Real FerroX::gamma; // gamma = 6*alpha_111
Expand Down Expand Up @@ -284,6 +287,16 @@ void InitializeFerroXNamespace(const amrex::GpuArray<amrex::Real, AMREX_SPACEDIM
pp.get("epsilonZ_fe",epsilonZ_fe);// epsilon_r for FE
pp.get("epsilon_de",epsilon_de);// epsilon_r for DE
pp.get("epsilon_si",epsilon_si);// epsilon_r for SC

epsilon_metal = 1.;
pp.query("epsilon_metal",epsilon_metal);// epsilon_r for metal

metal_screening_length = 1.e5;
pp.query("metal_screening_length",metal_screening_length);// metal_screening_length

metal_thickness = 0.;
pp.query("metal_thickness",metal_thickness);// metal_thickness

pp.get("alpha",alpha);
pp.get("beta",beta);
pp.get("gamma",FerroX::gamma);
Expand Down
3 changes: 3 additions & 0 deletions Source/FerroX_namespace.H
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Expand Up @@ -23,6 +23,9 @@ namespace FerroX {
extern AMREX_GPU_MANAGED amrex::Real epsilonZ_fe;
extern AMREX_GPU_MANAGED amrex::Real epsilon_de;
extern AMREX_GPU_MANAGED amrex::Real epsilon_si;
extern AMREX_GPU_MANAGED amrex::Real epsilon_metal;
extern AMREX_GPU_MANAGED amrex::Real metal_screening_length;
extern AMREX_GPU_MANAGED amrex::Real metal_thickness;
extern AMREX_GPU_MANAGED amrex::Real alpha; // alpha = 2*alpha_1
extern AMREX_GPU_MANAGED amrex::Real beta; // beta = 4*alpha_11
extern AMREX_GPU_MANAGED amrex::Real gamma; // gamma = 6*alpha_111
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7 changes: 7 additions & 0 deletions Source/Solver/TotalEnergyDensity.H
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Expand Up @@ -16,3 +16,10 @@ void CalculateTDGL_RHS(Array<MultiFab, AMREX_SPACEDIM> &GL_rhs,
const Geometry& geom,
const amrex::GpuArray<amrex::Real, AMREX_SPACEDIM>& prob_lo,
const amrex::GpuArray<amrex::Real, AMREX_SPACEDIM>& prob_hi);

void Compute_P_Sum(const std::array<MultiFab, AMREX_SPACEDIM>& P, Real& sum);

void Compute_P_index_Sum(const MultiFab& MaterialMask, Real& count);

void Compute_P_av(const std::array<MultiFab, AMREX_SPACEDIM>& P, Real& sum, const MultiFab& MaterialMask, Real& count, Real &P_av_z);

87 changes: 87 additions & 0 deletions Source/Solver/TotalEnergyDensity.cpp
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Expand Up @@ -14,6 +14,23 @@ void CalculateTDGL_RHS(Array<MultiFab, AMREX_SPACEDIM> &GL_rhs,
const amrex::GpuArray<amrex::Real, AMREX_SPACEDIM>& prob_lo,
const amrex::GpuArray<amrex::Real, AMREX_SPACEDIM>& prob_hi)
{

Real average_P_r = 0.;
Real total_P_r = 0.;
Real FE_index_counter = 0.;

Compute_P_av(P_old, total_P_r, MaterialMask, FE_index_counter, average_P_r);

//Calculate integrated electrode charge (Qe) based on eq 13 of https://pubs.aip.org/aip/jap/article/44/8/3379/6486/Depolarization-fields-in-thin-ferroelectric-films
Real FE_thickness = FE_hi[2] - FE_lo[2];
Real coth = (exp(2.*metal_thickness/metal_screening_length) + 1.0) / (exp(2.*metal_thickness/metal_screening_length) - 1.0);
Real csch = (2.*exp(metal_thickness/metal_screening_length)) / (exp(2.*metal_thickness/metal_screening_length) - 1.0);
Real numerator = 0.5 * FE_thickness * average_P_r / epsilonX_fe;
Real denominator = metal_screening_length/epsilon_de*(coth - csch) + FE_thickness/(2.*epsilonX_fe);
Real Qe = -numerator/denominator;
Real theta = -Qe/average_P_r;
//Real E_dep_metal = -average_P_r/epsilonX_fe*(1.0 - theta);

// loop over boxes
for ( MFIter mfi(P_old[0]); mfi.isValid(); ++mfi )
{
Expand Down Expand Up @@ -153,6 +170,7 @@ void CalculateTDGL_RHS(Array<MultiFab, AMREX_SPACEDIM> &GL_rhs,
( dFdPr_Landau
+ dFdPr_grad
- Er(i,j,k)
+ pOld_r(i,j,k)/epsilonX_fe*(1.0 - theta)
//+ DphiDz(phi, z_hi, z_lo, i, j, k, dx, prob_lo, prob_hi)
);

Expand All @@ -165,4 +183,73 @@ void CalculateTDGL_RHS(Array<MultiFab, AMREX_SPACEDIM> &GL_rhs,
}
}

void Compute_P_Sum(const std::array<MultiFab, AMREX_SPACEDIM>& P, Real& sum)
{

// Initialize to zero
sum = 0.;

ReduceOps<ReduceOpSum> reduce_op;

ReduceData<Real> reduce_data(reduce_op);
using ReduceTuple = typename decltype(reduce_data)::Type;

for (MFIter mfi(P[2],TilingIfNotGPU()); mfi.isValid(); ++mfi)
{
const Box& bx = mfi.tilebox();
const Box& bx_grid = mfi.validbox();

auto const& fab = P[2].array(mfi);

reduce_op.eval(bx, reduce_data,
[=] AMREX_GPU_DEVICE (int i, int j, int k) -> ReduceTuple
{
return {fab(i,j,k)};
});
}

sum = amrex::get<0>(reduce_data.value());
ParallelDescriptor::ReduceRealSum(sum);
}


void Compute_P_index_Sum(const MultiFab& MaterialMask, Real& count)
{

// Initialize to zero
count = 0.;

ReduceOps<ReduceOpSum> reduce_op;

ReduceData<Real> reduce_data(reduce_op);
using ReduceTuple = typename decltype(reduce_data)::Type;

for (MFIter mfi(MaterialMask, TilingIfNotGPU()); mfi.isValid(); ++mfi)
{
const Box& bx = mfi.tilebox();
const Box& bx_grid = mfi.validbox();

auto const& fab = MaterialMask.array(mfi);

reduce_op.eval(bx, reduce_data,
[=] AMREX_GPU_DEVICE (int i, int j, int k) -> ReduceTuple
{
if(fab(i,j,k) == 0.) {
return {1.};
} else {
return {0.};
}

});
}

count = amrex::get<0>(reduce_data.value());
ParallelDescriptor::ReduceRealSum(count);
}

void Compute_P_av(const std::array<MultiFab, AMREX_SPACEDIM>& P, Real& sum, const MultiFab& MaterialMask, Real& count, Real& P_av_z)
{
Compute_P_Sum(P, sum);
Compute_P_index_Sum(MaterialMask, count);
P_av_z = sum/count;
}