private static double SigularAnalitycalMajchrzak(double denominator2, Segment segmentR, CollocationPoint collPointR, Segment segmentI, CollocationPoint collPointI)
{
var destx = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().x + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().x;
var desty = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().y + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().y;
var dest = (double)Math.Sqrt((segmentI.ShapeFunction.GetV0().x - destx) * (segmentI.ShapeFunction.GetV0().x - destx) + (segmentI.ShapeFunction.GetV0().y - desty) * (segmentI.ShapeFunction.GetV0().y - desty));
return(0.5 * CzebyshewSeries.calculate(dest, collPointI.Index));
}
public double CalculateValue(double Point)
{
double result = 0.0;
for (int j = 0; j < degree; j++)
{
result += this.BoundaryConditionVector[j] * CzebyshewSeries.calculate(Point, j);
}
return(result);
}
private static double SigularAnalitycalMajchrzak(double denominator1, double denominator2, Segment segmentR, CollocationPoint collPointR, Segment segmentI, CollocationPoint collPointI)
{
var destx = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().x + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().x;
var desty = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().y + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().y;
var dest = (double)Math.Sqrt((segmentI.ShapeFunction.GetV0().x - destx) * (segmentI.ShapeFunction.GetV0().x - destx) + (segmentI.ShapeFunction.GetV0().y - desty) * (segmentI.ShapeFunction.GetV0().y - desty));
var beta = Math.Pow(segmentI.Lenght, 2.0) / (4.0 * denominator1);
double value = 2.0 / denominator2 * (2.0 - FunctionEi.gamma - Math.Log10(beta) + (beta * FunctionEi.w[0]) / 3.0 + (Math.Pow(beta, 2) * FunctionEi.w[1]) / 5.0
+ (Math.Pow(beta, 3) * FunctionEi.w[2]) / 7.0 + (Math.Pow(beta, 4) * FunctionEi.w[3]) / 9.0 + (Math.Pow(beta, 5) * FunctionEi.w[4]) / 11.0);
value *= CzebyshewSeries.calculate(dest, collPointI.Index);
return value;
}
private static double CalculateCore(RealPoint point, BoundaryIntegrationPoint integrationPoint, double denominator1, double denominator2, Segment segment, CollocationPoint collPoint)
{
double lambda1 = point.x - integrationPoint.RealPosition.x;
double lambda2 = point.y - integrationPoint.RealPosition.y;
double r2 = (double)(lambda1 * lambda1 + lambda2 * lambda2);
double a = (double)r2 / denominator1;
return (double)(integrationPoint.QuadratureValue
* CzebyshewSeries.calculate(integrationPoint.ParametricPosition * segment.Lenght, collPoint.Index)
* integrationPoint.Jacobian
* (FunctionEi.calculate(a) / denominator2));
}
private static double functionF(BezieCurve boundaryShape, double s, double s1, double denominator2, int collPointIndex)
{
var n = boundaryShape.CalculateNormalVector(s);
double L = (boundaryShape.a1.x + (s1 + s) * boundaryShape.a2.x + (s1 * s1 + s * s1 + s * s) * boundaryShape.a3.x) * n.X +
(boundaryShape.a1.y + (s1 + s) * boundaryShape.a2.y + (s1 * s1 + s * s1 + s * s) * boundaryShape.a3.y) * n.Y;
double M = Math.Pow((boundaryShape.a1.x + (s1 + s) * boundaryShape.a2.x + (s1 * s1 + s * s1 + s * s) * boundaryShape.a3.x), 2) +
Math.Pow((boundaryShape.a1.y + (s1 + s) * boundaryShape.a2.y + (s1 * s1 + s * s1 + s * s) * boundaryShape.a3.y), 2);
double r2 = Math.Pow(s1 * boundaryShape.lenght - s * boundaryShape.lenght, 2) * M;
double f = L / M
* Math.Exp(-r2 / denominator2)
* CzebyshewSeries.calculate(s * boundaryShape.lenght, collPointIndex);
return(f);
}
private static double CalculateCore(double denominator2, RealPoint point, BoundaryIntegrationPoint integrationPoint, Segment segment, CollocationPoint collPoint)
{
double lambda1 = point.x - integrationPoint.RealPosition.x;
double lambda2 = point.y - integrationPoint.RealPosition.y;
double r2 = (double)(lambda1 * lambda1 + lambda2 * lambda2);
double d = (double)(lambda1 * integrationPoint.NormalVector.X + lambda2 * integrationPoint.NormalVector.Y);
double denomiantor1 = (double)4.0 * Math.PI * r2;
double core = (double)d / denomiantor1 * Math.Exp(-r2 / denominator2);
return((double)(integrationPoint.QuadratureValue
* CzebyshewSeries.calculate(integrationPoint.ParametricPosition * segment.Lenght, collPoint.Index)
* integrationPoint.Jacobian
* core));
}
private static double SigularSeparate(double denominator2, Segment segmentR, CollocationPoint collPointR, Segment segmentI, CollocationPoint collPointI)
{
double value = 0.0;
///TODO: Sprawdzić jak dla nieliniowych ma być
var destx = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().x + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().x;
var desty = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().y + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().y;
var dest = (double)Math.Sqrt((segmentI.ShapeFunction.GetV0().x - destx) * (segmentI.ShapeFunction.GetV0().x - destx) + (segmentI.ShapeFunction.GetV0().y - desty) * (segmentI.ShapeFunction.GetV0().y - desty));
value = 0.5 * CzebyshewSeries.calculate(dest, collPointI.Index);
for (int singularIndex1 = 0; singularIndex1 < segmentI.SingularBoundaryIntegrationPointsCount; singularIndex1++)
{
var singularIntegrationPoint = new BoundaryIntegrationPoint(
singularIndex1,
segmentI.GaussQuadratureForSingularIntegral.xi[singularIndex1],
0.0,
collPointR.ParametricPosition,
segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1],
segmentI.ShapeFunction);
value += (double)((collPointR.ParametricPosition) * CalculateCore(denominator2, collPointR.RealPosition, singularIntegrationPoint, segmentI, collPointI));
}
for (int singularIndex1 = 0; singularIndex1 < segmentI.SingularBoundaryIntegrationPointsCount; singularIndex1++)
{
var singularIntegrationPoint = new BoundaryIntegrationPoint(
singularIndex1,
segmentI.GaussQuadratureForSingularIntegral.xi[singularIndex1],
collPointR.ParametricPosition,
1.0,
segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1],
segmentI.ShapeFunction);
value += (double)((1.0 - collPointR.ParametricPosition) * CalculateCore(denominator2, collPointR.RealPosition, singularIntegrationPoint, segmentI, collPointI));
}
return(value);
}
private static double SigularSeparateWithAnalitycal(double denominator2, Segment segmentR, CollocationPoint collPointR, Segment segmentI, CollocationPoint collPointI)
{
double value = 0.0;
///TODO: Sprawdzić jak dla nieliniowych ma być
var destx = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().x + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().x;
var desty = (1 - collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV0().y + (collPointR.ParametricPosition) * segmentR.ShapeFunction.GetV1().y;
var dest = (double)Math.Sqrt((segmentI.ShapeFunction.GetV0().x - destx) * (segmentI.ShapeFunction.GetV0().x - destx) + (segmentI.ShapeFunction.GetV0().y - desty) * (segmentI.ShapeFunction.GetV0().y - desty));
value = 0.5 * CzebyshewSeries.calculate(dest, collPointI.Index);
double distance = segmentR.DistanceFromSingularPoint;
double a = collPointR.ParametricPosition - distance;
double b = collPointR.ParametricPosition + distance;
double I1 = 0.0;
double I2 = 0.0;
double s1 = collPointR.ParametricPosition;
var boundaryShape = (BezieCurve)segmentR.ShapeFunction;
for (int singularIndex1 = 0; singularIndex1 < segmentI.SingularBoundaryIntegrationPointsCount; singularIndex1++)
{
double w = 0.5 * (segmentI.GaussQuadratureForSingularIntegral.xi[singularIndex1] + 1.0);
double parametera = (a - s1) * w + s1;
double parameterb = (b - s1) * w + s1;
double sa = (parametera - a);
double sb = (parameterb - b);
I1 -= (functionF(boundaryShape, sa, s1, denominator2, collPointR.Index)
* segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1])
- (functionF(boundaryShape, s1, s1, denominator2, collPointR.Index)
* Math.Log(Math.Abs(a * boundaryShape.lenght - s1 * boundaryShape.lenght)));
I2 += (functionF(boundaryShape, sb, s1, denominator2, collPointR.Index)
* segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1])
+ (functionF(boundaryShape, s1, s1, denominator2, collPointR.Index)
* Math.Log(Math.Abs(b * boundaryShape.lenght - s1 * boundaryShape.lenght)));
}
value += (1.0 / (2.0 * Math.PI)) * (I1 + I2);
for (int singularIndex1 = 0; singularIndex1 < segmentI.SingularBoundaryIntegrationPointsCount; singularIndex1++)
{
var singularIntegrationPoint = new BoundaryIntegrationPoint(
singularIndex1,
segmentI.GaussQuadratureForSingularIntegral.xi[singularIndex1],
0.0,
a,
segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1],
segmentI.ShapeFunction);
value += (double)((collPointR.ParametricPosition) * CalculateCore(denominator2, collPointR.RealPosition, singularIntegrationPoint, segmentI, collPointI));
}
for (int singularIndex1 = 0; singularIndex1 < segmentI.SingularBoundaryIntegrationPointsCount; singularIndex1++)
{
var singularIntegrationPoint = new BoundaryIntegrationPoint(
singularIndex1,
segmentI.GaussQuadratureForSingularIntegral.xi[singularIndex1],
b,
1.0,
segmentI.GaussQuadratureForSingularIntegral.Ai[singularIndex1],
segmentI.ShapeFunction);
value += (double)((1.0 - collPointR.ParametricPosition) * CalculateCore(denominator2, collPointR.RealPosition, singularIntegrationPoint, segmentI, collPointI));
}
return(value);
}
