public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation, IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
int numDofs = nodes.Count;
var stiffness = Vector.CreateZero(numDofs);
IReadOnlyList <double[]> shapeFunctions =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
for (int gp = 0; gp < integration.IntegrationPoints.Count; ++gp)
{
Vector shapeFunctionVector = Vector.CreateFromArray(shapeFunctions[gp]);
Matrix jacobianMatrix = Matrix.CreateZero(2, 3);
for (int k = 0; k < nodes.Count; k++)
{
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][k, 0] * nodes[k].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][k, 0] * nodes[k].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][k, 0] * nodes[k].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][k, 1] * nodes[k].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][k, 1] * nodes[k].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][k, 1] * nodes[k].Z;
}
Vector tangentVector1 = jacobianMatrix.GetRow(0);
Vector tangentVector2 = jacobianMatrix.GetRow(1);
Vector normalVector = tangentVector1.CrossProduct(tangentVector2);
var jacdet = normalVector.Norm2();
double dA = jacdet * integration.IntegrationPoints[gp].Weight;
stiffness.AxpyIntoThis(shapeFunctionVector, dA);
}
var appliedDisplacements = Vector.CreateWithValue(nodes.Count, _flux);
var fluxLoad = stiffness.DoEntrywise(appliedDisplacements, (stiffi, appi) => stiffi * appi);
var table = new Table <INode, IDofType, double>();
for (int i = 0; i < nodes.Count; i++)
{
table.TryAdd(nodes[i], ThermalDof.Temperature, fluxLoad[i]);
}
return(table);
}
public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation, IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
//nodes[0].ElementsDictionary.Values.ToList<>
int numDofs = nodes.Count;
double kappaCoef;
if (numDofs == 4)
{
kappaCoef = 100;
}
else
{
kappaCoef = 1;
}
var stiffness = Matrix.CreateZero(numDofs, numDofs);
IReadOnlyList <double[]> shapeFunctions =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
double[] dist = new double[nodes.Count];
List <INode> neighborNodes = new List <INode>();
for (int i = 0; i < nodes.Count; i++)
{
neighborNodes.Clear();
foreach (var element in nodes[i].ElementsDictionary.Values)
{
neighborNodes.AddRange(element.Nodes);
}
neighborNodes = neighborNodes.Distinct().ToList();
neighborNodes.Remove(nodes[i]);
var minDist = neighborNodes.Select(x => Math.Sqrt(
Math.Pow(nodes[i].X - x.X, 2) +
Math.Pow(nodes[i].Y - x.Y, 2) + Math.Pow(nodes[i].Z - x.Z, 2))).Min();
dist[i] = minDist;
}
//double kappa = kappaCoef * _diffusionCoeff / dist.Min();
//double[] kappa = new double[nodes.Count];
for (int gp = 0; gp < integration.IntegrationPoints.Count; ++gp)
{
//var jacobian = new IsoparametricJacobian3D(Nodes, shapeGradientsNatural[gp]);
var shapeFunctionMatrix = Vector.CreateFromArray(shapeFunctions[gp]);
Matrix jacobianMatrix = Matrix.CreateZero(2, 3);
for (int k = 0; k < nodes.Count; k++)
{
//xGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].X;
//yGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].Y;
//zGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].Z;
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][k, 0] * nodes[k].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][k, 0] * nodes[k].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][k, 0] * nodes[k].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][k, 1] * nodes[k].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][k, 1] * nodes[k].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][k, 1] * nodes[k].Z;
//kappa[k] = _diffusionCoeff / .05 / dist[k];
}
Vector tangentVector1 = jacobianMatrix.GetRow(0);
Vector tangentVector2 = jacobianMatrix.GetRow(1);
Vector normalVector = tangentVector1.CrossProduct(tangentVector2);
var jacdet = normalVector.Norm2();
normalVector.ScaleIntoThis(1 / jacdet);
Matrix jacobianMatrixLeftInverse = jacobianMatrix.Transpose() *
(jacobianMatrix * jacobianMatrix.Transpose()).Invert();
Matrix shapeGradientsCartesian = (shapeGradientsNatural[gp]) * jacobianMatrixLeftInverse.Transpose();
Matrix deformation = shapeGradientsCartesian.Transpose();
Vector deformationNormal = normalVector * deformation;
//Vector deformationX = deformation.GetRow(0);
//Vector deformationY = deformation.GetRow(1);
//Vector deformationZ = deformation.GetRow(2);
//Matrix partial = kappa * shapeFunctionMatrix.TensorProduct(shapeFunctionMatrix)
// -_diffusionCoeff * deformationNormal.TensorProduct(shapeFunctionMatrix);
double kappa = _diffusionCoeff / .05;
Matrix partial = kappa * shapeFunctionMatrix.TensorProduct(shapeFunctionMatrix);
//Vector surfaceBasisVector1 = Vector.CreateZero(3);
//surfaceBasisVector1[0] = jacobianMatrix[0, 0];
//surfaceBasisVector1[1] = jacobianMatrix[0, 1];
//surfaceBasisVector1[2] = jacobianMatrix[0, 2];
//Vector surfaceBasisVector2 = Vector.CreateZero(3);
//surfaceBasisVector2[0] = jacobianMatrix[1, 0];
//surfaceBasisVector2[1] = jacobianMatrix[1, 1];
//surfaceBasisVector2[2] = jacobianMatrix[1, 2];
//Vector surfaceBasisVector3 = surfaceBasisVector1.CrossProduct(surfaceBasisVector2);
//var jacdet = surfaceBasisVector3.Norm2();
double dA = jacdet * integration.IntegrationPoints[gp].Weight;
stiffness.AxpyIntoThis(partial, dA);
}
//var appliedDisplacements=Vector.CreateWithValue(nodes.Count, _magnitude);
var appliedDisplacements = _distribution(nodes);
var weakDirichletForces = stiffness * appliedDisplacements;
var table = new Table <INode, IDofType, double>();
for (int i = 0; i < nodes.Count; i++)
{
table.TryAdd(nodes[i], ThermalDof.Temperature, weakDirichletForces[i]);
}
return(table);
}
public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation,
IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
var loadTable = new Table <INode, IDofType, double>();
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
IReadOnlyList <double[]> shapeFunctionNatural =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
for (int gp = 0; gp < integration.IntegrationPoints.Count; gp++)
{
var jacobianMatrix = Matrix.CreateZero(2, 3);
for (int indexNode = 0; indexNode < nodes.Count; indexNode++)
{
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].Z;
}
var tangentVector1 = jacobianMatrix.GetRow(0);
var tangentVector2 = jacobianMatrix.GetRow(1);
var normalVector = tangentVector1.CrossProduct(tangentVector2);
Vector surfaceBasisVector1 = Vector.CreateZero(3);
surfaceBasisVector1[0] = jacobianMatrix[0, 0];
surfaceBasisVector1[1] = jacobianMatrix[0, 1];
surfaceBasisVector1[2] = jacobianMatrix[0, 2];
Vector surfaceBasisVector2 = Vector.CreateZero(3);
surfaceBasisVector2[0] = jacobianMatrix[1, 0];
surfaceBasisVector2[1] = jacobianMatrix[1, 1];
surfaceBasisVector2[2] = jacobianMatrix[1, 2];
Vector surfaceBasisVector3 = surfaceBasisVector1.CrossProduct(surfaceBasisVector2);
var jacdet = surfaceBasisVector3.Norm2();
var weightFactor = integration.IntegrationPoints[gp].Weight;
for (int indexNode = 0; indexNode < nodes.Count; indexNode++)
{
var node = nodes[indexNode];
var valueX = _loadX * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
var valueY = _loadY * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
var valueZ = _loadZ * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
if (loadTable.Contains(node, StructuralDof.TranslationX))
{
loadTable[node, StructuralDof.TranslationX] += valueX;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationX, valueX);
}
if (loadTable.Contains(node, StructuralDof.TranslationY))
{
loadTable[node, StructuralDof.TranslationY] += valueY;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationY, valueY);
}
if (loadTable.Contains(node, StructuralDof.TranslationZ))
{
loadTable[node, StructuralDof.TranslationZ] += valueZ;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationZ, valueZ);
}
}
}
return(loadTable);
}