public double U(Point p)
{
FiniteElement element = null;
foreach (FiniteElement e in Info.Mesh)
{
if (Utilities.PointInsideTriangle(Info.Points[e.V1], Info.Points[e.V2], Info.Points[e.V3], p))
{
element = e;
break;
}
}
if (element != null)
{
(double L1, double L2, double L3) = Utilities.GetL(Info.Points[element.V1], Info.Points[element.V2], Info.Points[element.V3], p);
double result = 0.0;
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
result += Weights[element.Vertices[i]] * FEMInfo.LBasis[i](L1, L2, L3);
}
return(result);
}
return(0.0);
}
void AddLocalToGlobal(IMatrix A, double[] B, FiniteElement e)
{
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
A.DI[e.Vertices[i]] += local[i, i];
B[e.Vertices[i]] += localb[i];
for (int j = 0; j < i; j++)
{
int a = e.Vertices[i];
int b = e.Vertices[j];
if (a < b)
{
(a, b) = (b, a);
}
if (A.IA[a + 1] > A.IA[a])
{
Span <int> span = new Span <int>(A.JA, A.IA[a], A.IA[a + 1] - A.IA[a]);
int k;
for (k = 0; k < A.IA[a + 1] - A.IA[a]; k++)
{
if (span[k] == b)
{
break;
}
}
int index = A.IA[a] + k;
A.AL[index] += local[i, j];
}
}
}
}
void BuildLocalB(FiniteElement e)
{
Point a = Info.Points[e.V1];
Point b = Info.Points[e.V2];
Point c = Info.Points[e.V3];
Point[] coords = Utilities.TriangleCubicPoints(a, b, c);
double D = Math.Abs(Utilities.Det(a, b, c));
double[] temp = new double[FEMInfo.BasisSize];
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
temp[i] = Info.F(coords[i].R, coords[i].Z);
}
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
localb[i] = temp[0] * M[i][0];
for (int j = 1; j < FEMInfo.BasisSize; j++)
{
localb[i] += temp[j] * M[i][j];
}
localb[i] *= D;
}
}
void BuildLocalMatrix(FiniteElement e)
{
Point a = Info.Points[e.V1];
Point b = Info.Points[e.V2];
Point c = Info.Points[e.V3];
double D = Math.Abs(Utilities.Det(a, b, c));
double[] alpha = Utilities.Alpha(a, b, c);
Grad[] grads = new Grad[3]
{
new Grad(alpha[0], alpha[1]),
new Grad(alpha[2], alpha[3]),
new Grad(alpha[4], alpha[5])
};
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
Array.Fill(M[i], 0.0);
}
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
for (int j = 0; j < FEMInfo.BasisSize; j++)
{
double G = 0;
foreach (FEMInfo.LocalCompG comp in gPattern[i, j])
{
double scalGrad = grads[comp.Grad1].R * grads[comp.Grad2].R + grads[comp.Grad1].Z * grads[comp.Grad2].Z;
G += comp.Coefficient * scalGrad * Info.Points[e.Vertices[comp.Rnum]].R;
}
foreach (FEMInfo.LocalCompM comp in mPattern[i, j])
{
M[i][j] += comp.Coefficient * Info.Points[e.Vertices[comp.Rnum]].R;
}
local[i, j] = (e.Material.Gamma * M[i][j] + e.Material.Sigma * G) * D;
}
}
}
void BuildLocalB(FiniteElement e)
{
Point a = Info.Points[e.V1];
Point b = Info.Points[e.V2];
Point c = Info.Points[e.V3];
Point[] coords = Utilities.TriangleCubicPoints(a, b, c);
for (int i = 0; i < FEMInfo.BasisSize; i++)
{
if (Math.Abs(coords[i].R - Info.R0) < 1.0e-15 && Math.Abs(coords[i].Z - Info.Z0) < 1.0e-15)
{
localb[i] = 1.0 * Info.DeltaCoefficient;
}
else
{
localb[i] = 0.0;
}
}
}
public void Analys(List <Node> nodes, List <Triangle> triangles, int nx, int ny)
{
// Собственно метод МКЭ: сборка и решение СЛАУ
K = new DenseMatrix(nodes.Count);
F = new DenseVector(nodes.Count);
FiniteElement element = new FiniteElement();
// Ансамблирование
// Цикл по всем КЭ
for (int k = 0; k < triangles.Count; k++)
{
Triangle tr = triangles[k];
// Локальная матрица жетскости КЭ
DenseMatrix Ke = element.ElementMatrix(nodes[tr.nodes[0]], nodes[tr.nodes[1]], nodes[tr.nodes[2]]);
// Локальный вектор нагрузок КЭ
DenseVector Fe = element.GetVector();
// Добавление локальной матрицы к глобальной
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
K[tr.nodes[i], tr.nodes[j]] += Ke[i, j];
}
// Добавление локального вектора к глобальному
if (nodes[tr.nodes[i]].isload)
{
F[tr.nodes[i]] += nodes[tr.nodes[i]].load * Fe[i];
}
}
}
// Внесение в систему граничных условий
for (int i = 0; i < nodes.Count; i++)
{
if (!nodes[i].boundary)
{
continue;
}
for (int j = 0; j < nodes.Count; j++)
{
F[j] -= nodes[i].value * K[j, i];
K[i, j] = 0;
K[j, i] = 0;
}
K[i, i] = 1;
F[i] = nodes[i].value;
}
// Решение системы
DenseVector x = (DenseVector)K.LU().Solve(F);
// Вывод результатов в файл
FileStream fs = File.Create("all.txt");
StreamWriter sw = new StreamWriter(fs);
for (int i = 0; i < nx + 1; i++)
{
for (int j = 0; j < ny + 1; j++)
{
int k = i * (ny + 1) + j;
double err = Math.Abs(1 - x[k] / Fan(nodes[k].x, nodes[k].y));
String s = String.Format(CultureInfo.CreateSpecificCulture("en-US"),
"{0,14:E} {1,14:E} {2,14:E} {3,14:E}",
nodes[k].x, nodes[k].y, x[k], err);
sw.WriteLine(s);
}
sw.WriteLine();
}
sw.Close();
fs.Close();
}