/// <summary>
/// Generates a laplacian matrix in one-dimension on a regular grid with Dirichlet BCs wot varying permitivity
/// </summary>
DoubleTriDiagMatrix Generate_Laplacian(ILayer[] layers)
{
DoubleTriDiagMatrix result = new DoubleTriDiagMatrix(exp.Nz_Pot, exp.Nz_Pot);
double factor_plus, factor_minus;
// cycle through the structure and fill in the Laplacian with the correct permittivities
for (int i = 1; i < exp.Nz_Pot - 1; i++)
{
double eps_plus = Geom_Tool.GetLayer(layers, i * exp.Dz_Pot + 0.5 * exp.Dz_Pot + exp.Zmin_Pot).Permitivity;
double eps_minus = Geom_Tool.GetLayer(layers, i * exp.Dz_Pot - 0.5 * exp.Dz_Pot + exp.Zmin_Pot).Permitivity;
// the factor which multiplies the Laplace equation
factor_plus = eps_plus / (exp.Dz_Pot * exp.Dz_Pot);
factor_minus = eps_minus / (exp.Dz_Pot * exp.Dz_Pot);
// on-diagonal term
result[i, i] = -1.0 * factor_minus + -1.0 * factor_plus;
// off-diagonal
result[i, i - 1] = 1.0 * factor_minus;
result[i, i + 1] = 1.0 * factor_plus;
}
// and fix boundary conditions
double factor = Geom_Tool.GetLayer(layers, exp.Zmin_Pot).Permitivity / (exp.Dz_Pot * exp.Dz_Pot);
result[0, 0] = 1.0 * factor;
result[0, 1] = 0.0;
factor = Geom_Tool.GetLayer(layers, (exp.Nz_Pot - 1) * exp.Dz_Pot + exp.Zmin_Pot).Permitivity / (exp.Dz_Pot * exp.Dz_Pot);
result[exp.Nz_Pot - 1, exp.Nz_Pot - 1] = 1.0 * factor;
result[exp.Nz_Pot - 1, exp.Nz_Pot - 2] = 0.0;
return(result);
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data g_phi)
{
DoubleTriDiagMatrix lap_mat = -1.0 * Generate_Laplacian(exp.Layers);
Band_Data rho_prime_spin_summed = rho_prime.Spin_Summed_Data;
// check that lap_mat and rho_prime have the same dimension
if (rho_prime_spin_summed.Length != lap_mat.Rows)
{
throw new Exception("Error - the Laplacian generated by pois_solv has a different order to rho_prime!");
}
for (int i = 0; i < rho_prime_spin_summed.Length; i++)
{
lap_mat[i, i] -= rho_prime_spin_summed.vec[i];
}
DoubleTriDiagFact lu_newt_step = new DoubleTriDiagFact(lap_mat);
// calculate newton step and its laplacian
Band_Data result = new Band_Data(lu_newt_step.Solve(-1.0 * g_phi.vec));
result.Laplacian = Calculate_Phi_Laplacian(result);
return(result);
}
public OneD_PoissonSolver(Experiment exp, bool using_external_code, Dictionary<string, object> input)
: base(using_external_code)
{
this.exp = exp;
// generate Laplacian matrix (spin-resolved)
if (!using_external_code)
{
laplacian = Generate_Laplacian(exp.Layers);
lu_fact = new DoubleTriDiagFact(laplacian);
}
}
public OneD_PoissonSolver(Experiment exp, bool using_external_code, Dictionary <string, object> input)
: base(using_external_code)
{
this.exp = exp;
// generate Laplacian matrix (spin-resolved)
if (!using_external_code)
{
laplacian = Generate_Laplacian(exp.Layers);
lu_fact = new DoubleTriDiagFact(laplacian);
}
}
/// <summary>
/// Generates a laplacian matrix in one-dimension on a regular grid with Dirichlet BCs wot varying permitivity
/// </summary>
DoubleTriDiagMatrix Generate_Laplacian(ILayer[] layers)
{
DoubleTriDiagMatrix result = new DoubleTriDiagMatrix(exp.Nz_Pot, exp.Nz_Pot);
double factor_plus, factor_minus;
// cycle through the structure and fill in the Laplacian with the correct permittivities
for (int i = 1; i < exp.Nz_Pot - 1; i++)
{
double eps_plus = Geom_Tool.GetLayer(layers, i * exp.Dz_Pot + 0.5 * exp.Dz_Pot + exp.Zmin_Pot).Permitivity;
double eps_minus = Geom_Tool.GetLayer(layers, i * exp.Dz_Pot - 0.5 * exp.Dz_Pot + exp.Zmin_Pot).Permitivity;
// the factor which multiplies the Laplace equation
factor_plus = eps_plus / (exp.Dz_Pot * exp.Dz_Pot);
factor_minus = eps_minus / (exp.Dz_Pot * exp.Dz_Pot);
// on-diagonal term
result[i, i] = -1.0 * factor_minus + -1.0 * factor_plus;
// off-diagonal
result[i, i - 1] = 1.0 * factor_minus;
result[i, i + 1] = 1.0 * factor_plus;
}
// and fix boundary conditions
double factor = Geom_Tool.GetLayer(layers, exp.Zmin_Pot).Permitivity / (exp.Dz_Pot * exp.Dz_Pot);
result[0, 0] = 1.0 * factor;
result[0, 1] = 0.0;
factor = Geom_Tool.GetLayer(layers, (exp.Nz_Pot - 1) * exp.Dz_Pot + exp.Zmin_Pot).Permitivity / (exp.Dz_Pot * exp.Dz_Pot);
result[exp.Nz_Pot - 1, exp.Nz_Pot - 1] = 1.0 * factor;
result[exp.Nz_Pot - 1, exp.Nz_Pot - 2] = 0.0;
return result;
}
// protected override Band_Data Get_ChemPot_From_External(Band_Data density)
// {
// Save_Data(density, dens_filename);
//
// return Get_Data_From_External(flexpde_script, initcalc_result_filename);
// }
/// <summary>
/// Calculates the Laplacian for the given band structure of the input potential
/// ie. returns d(eps * d(input))
/// NOTE: the input should be a potential so make sure you divide all band energies by q_e
/// </summary>
public Band_Data Calculate_Phi_Laplacian(Band_Data input)
{
DoubleTriDiagMatrix lap_mat = Generate_Laplacian(exp.Layers);
return(new Band_Data(MatrixFunctions.Product(lap_mat, input.vec)));
}
