private Matrix GenereteMatrix(List <Element> elem)
{
var n = elem.Count;
var matrix = new DenseMatrix(n + 1, n + 1);
matrix[0, 0] = Mu.Evaluate(elem[0].MidPoint) / elem[0].H - Beta.Evaluate(elem[0].MidPoint) / 2 + Sigma.Evaluate(elem[0].MidPoint) * elem[0].H / 3 + Alpha;
matrix[0, 1] = -Mu.Evaluate(elem[0].MidPoint) / elem[0].H + Beta.Evaluate(elem[0].MidPoint) / 2 + Sigma.Evaluate(elem[0].MidPoint) * elem[0].H / 6;
for (int i = 1; i < n; ++i)
{
matrix[i, i - 1] = -Mu.Evaluate(elem[i - 1].MidPoint) / elem[i - 1].H - Beta.Evaluate(elem[i - 1].MidPoint) / 2 + Sigma.Evaluate(elem[i - 1].MidPoint) * elem[i - 1].H / 6;
matrix[i, i] = Mu.Evaluate(elem[i - 1].MidPoint) / elem[i - 1].H + Beta.Evaluate(elem[i - 1].MidPoint) / 2 + Sigma.Evaluate(elem[i - 1].MidPoint) * elem[i - 1].H / 3 + Mu.Evaluate(elem[i].MidPoint) / elem[i].H - Beta.Evaluate(elem[i].MidPoint) / 2 + Sigma.Evaluate(elem[i].MidPoint) * elem[i].H / 3;
matrix[i, i + 1] = -Mu.Evaluate(elem[i].MidPoint) / elem[i].H + Beta.Evaluate(elem[i].MidPoint) / 2 + Sigma.Evaluate(elem[i].MidPoint) * elem[i].H / 6;
}
matrix[n, n - 1] = -Mu.Evaluate(elem[n - 1].MidPoint) / elem[n - 1].H - Beta.Evaluate(elem[n - 1].MidPoint) / 2 + Sigma.Evaluate(elem[n - 1].MidPoint) * elem[n - 1].H / 6;
matrix[n, n] = Mu.Evaluate(elem[n - 1].MidPoint) / elem[n - 1].H + Beta.Evaluate(elem[n - 1].MidPoint) / 2 + Sigma.Evaluate(elem[n - 1].MidPoint) * elem[n - 1].H / 3 + Gamma;
return(matrix);
}
private void CalculateErrors(ref Iteration iter)
{
var n = iter.Elements.Count;
var errors = new DenseVector(n);
var errorsNorms = new DenseVector(n);
var eNormV2 = 0.0;
var uNormV2 = 0.0;
for (int i = 0; i < n; ++i)
{
var m = Math.Pow(iter.Elements[i].H, 3) / Mu.Evaluate(iter.Elements[i].MidPoint);
var b = F.Evaluate(iter.Elements[i].MidPoint) - (Beta.Evaluate(iter.Elements[i].MidPoint) * iter.SolutionCenterDeriv[i]) - (Sigma.Evaluate(iter.Elements[i].MidPoint) * iter.SolutionCenter[i]);
var d = 10 + ((iter.Elements[i].H * Beta.Evaluate(iter.Elements[i].MidPoint)) / Mu.Evaluate(iter.Elements[i].MidPoint) * ((iter.Elements[i].H * iter.Elements[i].H * Sigma.Evaluate(iter.Elements[i].MidPoint)) / Mu.Evaluate(iter.Elements[i].MidPoint)));
var e_h2 = (5.0 / 6) * m * (b * b / d);
errorsNorms[i] = Math.Sqrt(Math.Abs(e_h2));
eNormV2 += Math.Abs(e_h2);
var q = iter.SolutionCenterDeriv[i];
uNormV2 += iter.Elements[i].H * q * q;
}
iter.UNormV2 = uNormV2;
iter.ENormV2 = eNormV2;
iter.ErrorsNormsV = errorsNorms;
//iter.UNorm = Math.Sqrt(uNormV2);
iter.UNorm = Math.Sqrt(iter.Solution * GenereteMatrix(iter.Elements) * iter.Solution);
iter.ENorm = Math.Sqrt(eNormV2);
for (int i = 0; i < n; ++i)
{
errors[i] = (errorsNorms[i] * Math.Sqrt(n) * 100) / Math.Sqrt(uNormV2 + eNormV2);
}
iter.Errors = errors;
if (iter.N == InitialN)
{
startEn = iter.ENorm;
}
iter.OrderOfConvergence = (iter.N != InitialN) ? (Math.Log(startEn) - Math.Log(iter.ENorm)) / (Math.Log(iter.N) - Math.Log(InitialN)) : 0;
iter.MaxRelativeError = iter.Errors.Maximum();
}