public void Perform()
{
var alfaDt = alfa * dt;
var dtAlfa = dt * (1 - alfa);
var primal = new double[dimension];
var timeSteps = Temperature.Length;
That = new double[dimension];
Tdot = new double[timeSteps][];
for (var i = 0; i < timeSteps; i++)
{
Tdot[i] = new double[dimension];
}
// calculate initial temperature gradients
var rhs = MatrixAlgebra.Mult(k, Temperature[0], profile);
for (var i = 0; i < dimension; i++)
{
Tdot[0][i] = (ForcingFunction[0][i] - rhs[i]) / c[i];
}
// evaluate constant coefficient matrix
var cm = new double[dimension][];
for (var row = 0; row < dimension; row++)
{
cm[row] = new double[row + 1 - profile[row]];
for (var col = 0; col <= (row - profile[row]); col++)
{
cm[row][col] = alfaDt * k[row][col];
}
cm[row][row - profile[row]] += c[row];
}
var profileSolverStatus =
new ProfileSolverStatus(cm, rhs, primal, status, profile);
profileSolverStatus.Decompose();
for (var counter = 1; counter < timeSteps; counter++)
{
// calculate temperature gradients at restrained nodes
for (var i = 0; i < dimension; i++)
{
if (status[i])
{
Tdot[counter][i] = (Temperature[counter][i] - Temperature[counter - 1][i]) / dt;
}
}
// calculate T(hat) for next step
for (var i = 0; i < dimension; i++)
{
if (status[i])
{
That[i] = Temperature[counter][i];
}
else
{
That[i] = Temperature[counter - 1][i] + dtAlfa * Tdot[counter - 1][i];
}
}
// modification of RHS
rhs = MatrixAlgebra.Mult(k, That, status, profile);
var rhSfr = MatrixAlgebra.MultUl(cm, Tdot[counter], status, profile);
for (var i = 0; i < dimension; i++)
{
rhs[i] = ForcingFunction[counter][i] - rhSfr[i] - rhs[i];
}
// backsubstitution
profileSolverStatus.SetRhs(rhs);
profileSolverStatus.SolvePrimal();
// temperatures and gradients at next time step for unrestrained nodes
for (var i = 0; i < dimension; i++)
{
if (status[i])
{
continue;
}
Tdot[counter][i] = primal[i];
Temperature[counter][i] = That[i] + alfaDt * primal[i];
}
}
}
