public static double Cphi1(Problem p, double t, double tau)
{
Vector<double> yVect = new Vector<double>();
Vector<double> x = new Vector<double>();
yVect.a = (double)p.Gamma1.a.DynamicInvoke(tau);
yVect.b = (double)p.Gamma1.b.DynamicInvoke(tau);
x.a = (double)p.Gamma2.a.DynamicInvoke(t);
x.b = (double)p.Gamma2.b.DynamicInvoke(t);
double a;
double b;
double rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
double rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
double rZero2 = rZero * rZero;
double rAP2 = rAP * rAP;
double rAStarP2 = rAStarP * rAStarP;
a = -(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a) / rAStarP2
- (x.a - yVect.a) / rAP2;
b = -(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b) / rAStarP2
- (x.b - yVect.b) / rAP2;
Vector<double> mju = p.NormalDerivative(x);
return (1/(2*Math.PI)) * (a * mju.a + b * mju.b);
}
public Solver(Problem pr, double mstep, int istep)
{
p = pr;
meshStep = mstep;
integralStep = istep;
GenerateMesh();
res = new Result();
}
public static double Dphi2(Problem p, double t, double tau)
{
Vector<double> xDeriv = new Vector<double>();
Vector<double> yVect = new Vector<double>();
Vector<double> x = new Vector<double>();
yVect.a = (double)p.Gamma2.a.DynamicInvoke(tau);
yVect.b = (double)p.Gamma2.b.DynamicInvoke(tau);
x.a = (double)p.Gamma2.a.DynamicInvoke(t);
x.b = (double)p.Gamma2.b.DynamicInvoke(t);
xDeriv.a = (double)p.Gamma2Derivative.a.DynamicInvoke(t);
xDeriv.b = (double)p.Gamma2Derivative.b.DynamicInvoke(t);
double rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
double rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
double rZero2 = rZero * rZero;
double rAP2 = rAP * rAP;
double rAStarP2 = rAStarP * rAStarP;
if (t != tau)
{
double a;
double b;
a = (p.R * p.R / rZero2) *
(x.a - (p.R * p.R / rZero2) * yVect.a) / Math.Pow(EuclidNorm(x.a - (p.R * p.R / rZero2) * yVect.a, x.b - (p.R * p.R / rZero2) * yVect.b), 2) -
(x.a - yVect.a) / Math.Pow(EuclidNorm(x.a - yVect.a, x.b - yVect.b), 2);
b = (p.R * p.R / rZero2) *
(x.b - (p.R * p.R / rZero2) * yVect.b) / Math.Pow(EuclidNorm(x.a - (p.R * p.R / rZero2) * yVect.a, x.b - (p.R * p.R / rZero2) * yVect.b), 2) -
(x.b - yVect.b) / Math.Pow(EuclidNorm(x.a - yVect.a, x.b - yVect.b), 2);
Vector<double> mju = p.NormalDerivative(x);
return (1 / (2 * Math.PI)) * (a * mju.a + b * mju.b);
}
else
{
Vector<double> mju = p.NormalDerivative(x);
double a;
double b;
double xDeriv2A = ((double)p.Gamma2Derivative.a.DynamicInvoke(t + 0.001) - (double)p.Gamma2Derivative.a.DynamicInvoke(t - 0.001)) * 2000;
double xDeriv2B = ((double)p.Gamma2Derivative.b.DynamicInvoke(t + 0.001) - (double)p.Gamma2Derivative.b.DynamicInvoke(t - 0.001)) * 2000;
a = (p.R * p.R / rZero2) *
(x.a - (p.R * p.R / rZero2) * yVect.a) / Math.Pow(EuclidNorm(x.a - (p.R * p.R / rZero2) * yVect.a, x.b - (p.R * p.R / rZero2) * yVect.b), 2) * mju.a -
(1 / 2d) * (xDeriv.b * xDeriv2A) / (Math.Pow(EuclidNorm(xDeriv.a, xDeriv.b), 3));
b = (p.R * p.R / rZero2) *
(x.b - (p.R * p.R / rZero2) * yVect.b) / Math.Pow(EuclidNorm(x.a - (p.R * p.R / rZero2) * yVect.a, x.b - (p.R * p.R / rZero2) * yVect.b), 2) * mju.b -
(1 / 2d) * (-xDeriv.a * xDeriv2B) / (Math.Pow(EuclidNorm(xDeriv.a, xDeriv.b), 3));
return (1 / (2 * Math.PI)) * (a + b);
}
}
public static double Aphi1(Problem p, double t,double tau, double n)
{
Vector<double> x = new Vector<double>();
Vector<double> yVect = new Vector<double>();
x.a = (double)p.Gamma1.a.DynamicInvoke(t);
x.b = (double)p.Gamma1.b.DynamicInvoke(t);
yVect.a = (double)p.Gamma1.a.DynamicInvoke(tau);
yVect.b = (double)p.Gamma1.b.DynamicInvoke(tau);
double rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
return Math.Log(p.R / rZero, Math.Exp(1)) - Math.Log(rAStarP, Math.Exp(1)) - H1(p, x, t, tau, n);
}
public static double[] Vector(int n, Problem p)
{
double[] vector = new double[2 * n];
double param = 2 * Math.PI / n;
for (int j = 0; j < n; j++)
{
vector[j] = IntegralsEvaluator.IntegralU0(p,new Vector<double>(
(double)p.Gamma1.a.DynamicInvoke(j * param),
(double)p.Gamma1.b.DynamicInvoke(j * param)));
vector[j + n] = IntegralsEvaluator.IntegralU0Der(p,new Vector<double>(
(double)p.Gamma2.a.DynamicInvoke(j * param),
(double)p.Gamma2.b.DynamicInvoke(j * param)));
}
return vector;
}
public static double IntegralU0Der(Problem p, Vector<double> x)
{
double sum = 0;
int count = 1;
double a = 0.5 * ((double)p.f0.DynamicInvoke(p.Gamma0(0).a, p.Gamma0(0).b))
* GreenFunction.NormalDerivative_Y_forU0(p, x, 0);
for (double i = 0.05; i < 2 * Math.PI; i += 0.05)
{
sum += (double)p.f0.DynamicInvoke(p.Gamma0(i).a, p.Gamma0(i).b)
* GreenFunction.NormalDerivative_Y_forU0(p, x, i);
count++;
}
double b = 0.5 * ((double)p.f0.DynamicInvoke(p.Gamma0(2 * Math.PI).a, p.Gamma0(2 * Math.PI).b))
* GreenFunction.NormalDerivative_Y_forU0(p, x, 2 * Math.PI);
//2*pi*R/count
return -(a + sum + b) * ((2 * Math.PI * p.R) / (double)count);
}
public static double[,] Matrix(int n, Problem p)
{
double[,] Matrix = new double[2 * n, 2 * n];
double param = 2 * Math.PI / n;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Matrix[i, j] = GreenFunction.Aphi1(p, i * param, j * param, n);
Matrix[i, j + n] = GreenFunction.Bphi2(p, i * param, j * param);
Matrix[i + n, j] = GreenFunction.Cphi1(p, i * param, j * param);
Matrix[i + n, j + n] = GreenFunction.Dphi2(p, i * param, j * param);
if (i == j)
Matrix[i, j] += 0.5;
}
}
return Matrix;
}
public static double Bphi2(Problem p, double t, double tau)
{
Vector<double> x = new Vector<double>();
Vector<double> yVect = new Vector<double>();
x.a = (double)p.Gamma1.a.DynamicInvoke(t);
x.b = (double)p.Gamma1.b.DynamicInvoke(t);
yVect.a = (double)p.Gamma2.a.DynamicInvoke(tau);
yVect.b = (double)p.Gamma2.b.DynamicInvoke(tau);
double rZero;
double rAP;
double rAStarP;
if (yVect.a == 0 && yVect.b == 0)
rZero = 0;
else
rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
if ((x.a == yVect.a) && (x.b == yVect.b))
rAP = 0;
else
rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
return Math.Log(p.R, Math.Exp(1)) - Math.Log(rZero, Math.Exp(1)) - Math.Log(rAStarP, Math.Exp(1)) + Math.Log(rAP, Math.Exp(1));
}
//can't be evaluated on Г0
public static double NormalDerivative_Y_forU0(Problem p, Vector<double> x , double t)
{
double GreenFunctionDer;
double a;
double b;
Vector<double> yVect = p.Gamma0(t);
Vector<double> yVectDeriv = p.Gamma0Derivative(t);
//Green Function Variables
double rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
double rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
double rZero2 = rZero * rZero;
double rAP2 = rAP * rAP;
double rAStarP2 = rAStarP * rAStarP;
//Constructing elements of the vector
//if (Math.Abs(rAP) > 1e-10)
//{
a = -(yVect.a / rZero2)
+ ((Math.Pow(p.R / rZero, 2)) * (x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a)) / rAStarP2
- (x.a - yVect.a) / rAP2;
b = -(yVect.b / rZero2)
+ ((Math.Pow(p.R / rZero, 2)) * (x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b)) / rAStarP2
- (x.b - yVect.b) / rAP2;
//}
//else
//{
// double yDeriv2A = (p.Gamma0Derivative(yVect.a + 0.001).a - p.Gamma0Derivative(yVect.a - 0.001).a) * 2000;
// double yDeriv2B = (p.Gamma0Derivative(yVect.b + 0.001).b - p.Gamma0Derivative(yVect.b - 0.001).b) * 2000;
// double yDerivNorm2 = yVectDeriv.a * yVectDeriv.a + yVectDeriv.b * yVectDeriv.b;
// a = -(yVect.a / rZero2)
// + ((Math.Pow(p.R / rZero, 2)) * (x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a)) / rAStarP2
// - (0.5 * yDeriv2A) / yDerivNorm2;
// b = -(yVect.b / rZero2)
// + ((Math.Pow(p.R / rZero, 2)) * (x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b)) / rAStarP2
// - (0.5 * yDeriv2B) / yDerivNorm2;
//}
//Count Mju function
Vector<double> mju = p.NormalDerivative(yVectDeriv);
//Count Green function
GreenFunctionDer = (1 / (2 * Math.PI)) * (a * mju.a + b * mju.b);
return GreenFunctionDer;
}
public static double NormalDerivative_X_Y_forU0(Problem p, Vector<double> x , double t)
{
return ND_X_Y_Part1(p, x, t) * ND_X_Y_Part2(p, x, t);
}
public static double ND_X_Y_Part2(Problem p, Vector<double> x, double t)
{
Vector<double> y = p.Gamma0(t);
//yVect.a = (double)p.Gamma2.a.DynamicInvoke(t);
//yVect.b = (double)p.Gamma2.b.DynamicInvoke(t);
double rZero = Math.Sqrt((Math.Pow(y.a, 2) + Math.Pow(y.b, 2)));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * y.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * y.b, 2));
Vector<double> mjux = p.NormalDerivative(x);
Vector<double> mjuy = p.NormalDerivative(y);
double rZero2 = rZero * rZero;
double rAStarP2 = rAStarP * rAStarP;
Vector<double> a = new Vector<double>(p.R * p.R / rAStarP2 * mjuy.a, p.R * p.R / rAStarP2 * mjuy.b);
double b = 2 * (p.R * p.R / rZero2 * ((x.a - y.a * (p.R * p.R / rZero2)) * mjuy.a + (x.b - y.b * (p.R * p.R / rZero2)) * mjuy.b)) / (rAStarP2 * rAStarP2);
return 1 / (2 * Math.PI) * (((a.a - b) * mjux.a) + ((a.b - b) * mjux.b));
}
public static double ND_X_Y_Part1(Problem p, Vector<double> x, double t)
{
Vector<double> y = p.Gamma0(t);
//yVect.a = (double)p.Gamma2.a.DynamicInvoke(t);
//yVect.b = (double)p.Gamma2.b.DynamicInvoke(t);
double rZero = Math.Sqrt((Math.Pow(y.a, 2) + Math.Pow(y.b, 2)));
double rAP = Math.Sqrt(Math.Pow(x.a - y.a, 2) + Math.Pow(x.b - y.b, 2));
Vector<double> mjux = p.NormalDerivative(x);
Vector<double> mjuy = p.NormalDerivative(y);
double rZero2 = rZero * rZero;
double rAP2 = rAP * rAP;
double a = (mjux.a * mjuy.a + mjux.b * mjuy.b) / rAP2;
double b = 2 * (((x.a - y.a) * mjuy.a + (x.b - y.b) * mjuy.b) / rAP2) * (((x.a - y.a) * mjux.a + (x.b - y.b) * mjux.b) / rAP2);
return 1 / (2 * Math.PI) * (a - b);
}
public static double H1(Problem p, Vector<double> x, double t, double tau, double n)
{
Vector<double> yVect = new Vector<double>();
yVect.a = (double)p.Gamma1.a.DynamicInvoke(tau);
yVect.b = (double)p.Gamma1.b.DynamicInvoke(tau);
Vector<double> xVectDer =new Vector<double>((double)p.Gamma1Derivative.a.DynamicInvoke(t), (double)p.Gamma1Derivative.b.DynamicInvoke(t));
if (t != tau)
{
double rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
return Math.Log(1 / rAP, Math.Exp(1));
}
else
{
//double norm = EuclidNorm((double)p.Gamma1Derivative.a.DynamicInvoke(tau), (double)p.Gamma1Derivative.b.DynamicInvoke(tau));
//return (-1 / 2d) * Math.Log((4 / Math.Exp(1)) * Math.Pow(Math.Sin((t - tau) / 2), 2), Math.Exp(1)) - 1 / 2 * Math.Log(2 * Math.Pow(norm, 2)) - 1 / 2d;
return -1 / 2d * Math.Pow((R(t, tau, n) - 1 / (2 * n) * Math.Log(Math.Pow(xVectDer.a, 2) + Math.Pow(xVectDer.a, 2), Math.Exp(1))), 2);
}
}
public static double GreenGamma2(Problem p, Vector<double> x, double t)
{
Vector<double> yVect = new Vector<double>();
yVect.a = (double)p.Gamma2.a.DynamicInvoke(t);
yVect.b = (double)p.Gamma2.b.DynamicInvoke(t);
//yVect.a = (double)p.Gamma2.a.DynamicInvoke(t);
//yVect.b = (double)p.Gamma2.b.DynamicInvoke(t);
double rZero = Math.Sqrt((Math.Pow(yVect.a, 2) + Math.Pow(yVect.b, 2)));
double rAP = Math.Sqrt(Math.Pow(x.a - yVect.a, 2) + Math.Pow(x.b - yVect.b, 2));
double rAStarP = Math.Sqrt(Math.Pow(x.a - (Math.Pow(p.R / rZero, 2)) * yVect.a, 2)
+ Math.Pow(x.b - (Math.Pow(p.R / rZero, 2)) * yVect.b, 2));
return Math.Log(p.R / rZero, Math.Exp(1)) - Math.Log(rAStarP, Math.Exp(1)) - Math.Log(1 / rAP, Math.Exp(1));
}