public virtual IMatrix2D StiffnessMatrix(IElement element)
{
double[,] coordinates = this.GetCoordinates(element);
GaussLegendrePoint3D[] integrationPoints = this.CalculateGaussMatrices(coordinates);
SymmetricMatrix2D stiffnessMatrix = new SymmetricMatrix2D(8);
int pointId = -1;
foreach (GaussLegendrePoint3D gaussPoint in integrationPoints)
{
pointId++;
IMatrix2D constitutiveMatrix = materialsAtGaussPoints[pointId].ConstitutiveMatrix;
double[,] b = gaussPoint.DeformationMatrix;
for (int i = 0; i < 8; i++)
{
double[] eb = new double[3];
for (int iE = 0; iE < 3; iE++)
{
eb[iE] = (constitutiveMatrix[iE, 0] * b[0, i]) + (constitutiveMatrix[iE, 1] * b[1, i]) +
(constitutiveMatrix[iE, 2] * b[2, i]);
}
for (int j = i; j < 8; j++)
{
double stiffness = (b[0, j] * eb[0]) + (b[1, j] * eb[1]) + (b[2, j] * eb[2]);
stiffnessMatrix[i, j] += stiffness * gaussPoint.WeightFactor;
}
}
}
return(stiffnessMatrix);
}
public double[] CalculateAccelerationForces(Element element, IList <MassAccelerationLoad> loads)
{
Vector <double> accelerations = new Vector <double>(6);
IMatrix2D <double> massMatrix = MassMatrix(element);
int index = 0;
foreach (MassAccelerationLoad load in loads)
{
foreach (DOFType[] nodalDOFTypes in dofs)
{
foreach (DOFType dofType in nodalDOFTypes)
{
if (dofType == load.DOF)
{
accelerations[index] += load.Amount;
}
index++;
}
}
}
double[] forces = new double[6];
massMatrix.Multiply(accelerations, forces);
return(forces);
}
public virtual IMatrix2D <double> StiffnessMatrix(Element element)
{
double[,] coordinates = this.GetCoordinates(element);
GaussLegendrePoint3D[] integrationPoints = this.CalculateGaussMatrices(coordinates);
SymmetricMatrix2D <double> stiffnessMatrix = new SymmetricMatrix2D <double>(24);
int pointId = -1;
foreach (GaussLegendrePoint3D intPoint in integrationPoints)
{
pointId++;
IMatrix2D <double> constitutiveMatrix = materialsAtGaussPoints[pointId].ConstitutiveMatrix;
double[,] b = intPoint.DeformationMatrix;
for (int i = 0; i < 24; i++)
{
double[] eb = new double[24];
for (int iE = 0; iE < 6; iE++)
{
eb[iE] = (constitutiveMatrix[iE, 0] * b[0, i]) + (constitutiveMatrix[iE, 1] * b[1, i]) +
(constitutiveMatrix[iE, 2] * b[2, i]) + (constitutiveMatrix[iE, 3] * b[3, i]) +
(constitutiveMatrix[iE, 4] * b[4, i]) + (constitutiveMatrix[iE, 5] * b[5, i]);
}
for (int j = i; j < 24; j++)
{
double stiffness = (b[0, j] * eb[0]) + (b[1, j] * eb[1]) + (b[2, j] * eb[2]) + (b[3, j] * eb[3]) +
(b[4, j] * eb[4]) + (b[5, j] * eb[5]);
stiffnessMatrix[i, j] += stiffness * intPoint.WeightFactor;
}
}
}
return(stiffnessMatrix);
}
public double[] CalculateForces(Element element, double[] localDisplacements, double[] localdDisplacements)
{
IMatrix2D <double> stiffnessMatrix = StiffnessMatrix(element);
Vector <double> disps = new Vector <double>(localDisplacements);
double[] forces = new double[localDisplacements.Length];
stiffnessMatrix.Multiply(disps, forces);
return(forces);
}
//private static int[] CalculateRowIndex(Subdomain subdomain)
//{
// return CalculateRowIndex(subdomain, subdomain.NodalDOFsDictionary);
//}
public static SkylineMatrix2D <double> CalculateGlobalMatrix(Subdomain subdomain, Dictionary <int, Dictionary <DOFType, int> > nodalDOFsDictionary, IElementMatrixProvider elementProvider)
{
// TODO: should encapsulate DOF logic into a separate entity that will manage things if embedded or not (should return element matrix and globaldofs correspondence list
var times = new Dictionary <string, TimeSpan>();
var totalStart = DateTime.Now;
SkylineMatrix2D <double> K = new SkylineMatrix2D <double>(GlobalMatrixAssemblerSkyline.CalculateRowIndex(subdomain, nodalDOFsDictionary));
times.Add("rowIndexCalculation", DateTime.Now - totalStart);
times.Add("element", TimeSpan.Zero);
times.Add("addition", TimeSpan.Zero);
foreach (Element element in subdomain.ElementsDictionary.Values)
{
var isEmbeddedElement = element.ElementType is IEmbeddedElement;
var elStart = DateTime.Now;
IMatrix2D <double> ElementK = elementProvider.Matrix(element);
times["element"] += DateTime.Now - elStart;
elStart = DateTime.Now;
var elementDOFTypes = element.ElementType.DOFEnumerator.GetDOFTypes(element);
var matrixAssemblyNodes = element.ElementType.DOFEnumerator.GetNodesForMatrixAssembly(element);
int iElementMatrixRow = 0;
for (int i = 0; i < elementDOFTypes.Count; i++)
{
Node nodeRow = matrixAssemblyNodes[i];
foreach (DOFType dofTypeRow in elementDOFTypes[i])
{
int dofRow = nodalDOFsDictionary.ContainsKey(nodeRow.ID) == false && isEmbeddedElement ? -1 : nodalDOFsDictionary[nodeRow.ID][dofTypeRow];
if (dofRow != -1)
{
int iElementMatrixColumn = 0;
for (int j = 0; j < elementDOFTypes.Count; j++)
{
Node nodeColumn = matrixAssemblyNodes[j];
foreach (DOFType dofTypeColumn in elementDOFTypes[j])
{
int dofColumn = nodalDOFsDictionary.ContainsKey(nodeColumn.ID) == false && isEmbeddedElement ? -1 : nodalDOFsDictionary[nodeColumn.ID][dofTypeColumn];
if (dofColumn != -1)
{
int height = dofRow - dofColumn;
if (height >= 0)
{
K.Data[K.RowIndex[dofRow] + height] += ElementK[iElementMatrixRow, iElementMatrixColumn];
}
}
iElementMatrixColumn++;
}
}
}
iElementMatrixRow++;
}
}
times["addition"] += DateTime.Now - elStart;
}
var totalTime = DateTime.Now - totalStart;
return(K);
}
public double[] CalculateForcesForLogging(Element element, double[] localDisplacements)
{
CalculateRotTranformation(element);
IMatrix2D <double> stiffnessMatrix = StiffnessMatrixPure(element);
var disps = rotTransformation * new Vector <double>(localDisplacements);
double[] forces = new double[disps.Length];
stiffnessMatrix.Multiply(disps, forces);
return(forces);
}
public ShapeNURBS2D(NURBSElement2D element, IGAModel model, IVector <double> parametricCoordinateKsi, IVector <double> parametricCoordinateHeta, IList <ControlPoint> controlPoints)
{
int numberOfCPHeta = model.KnotValueVectorHeta.Length - model.DegreeHeta - 1;
BSPLines1D bsplinesKsi = new BSPLines1D(model.DegreeKsi, model.KnotValueVectorKsi, parametricCoordinateKsi);
BSPLines1D bsplinesHeta = new BSPLines1D(model.DegreeHeta, model.KnotValueVectorHeta, parametricCoordinateHeta);
nurbsValues = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesKsi = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesHeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
int supportKsi = model.DegreeKsi + 1;
int supportHeta = model.DegreeHeta + 1;
int numberOfElementGaussPoints = (model.DegreeKsi + 1) * (model.DegreeHeta + 1);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
double sumKsiHeta = 0;
double sumdKsiHeta = 0;
double sumKsidHeta = 0;
for (int k = 0; k < numberOfElementGaussPoints; k++)
{
sumKsiHeta += bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
sumdKsiHeta = +bsplinesKsi.BSPLDerivativeValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
sumKsidHeta = +bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
}
for (int k = 0; k < numberOfElementGaussPoints; k++)
{
nurbsValues[k, i *supportHeta + j] = bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight / sumKsiHeta;
nurbsDerivativeValuesKsi[k, i *supportHeta + j] = bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] * controlPoints[k].Weight *
(bsplinesKsi.BSPLDerivativeValues[element.connectivity[k] / numberOfCPHeta, i] * sumKsiHeta -
bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] * sumdKsiHeta) / Math.Pow(sumKsiHeta, 2);
nurbsDerivativeValuesHeta[k, i *supportHeta + j] = bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
controlPoints[k].Weight *
(bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] * sumKsiHeta -
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] * sumKsidHeta) / Math.Pow(sumKsiHeta, 2);
}
}
}
}
private Sparse2D <double> BuildQFromSubdomain(Subdomain subdomain)
{
Sparse2D <double> qSubdomain = new Sparse2D <double>(subdomain.TotalDOFs, subdomain.TotalDOFs);
foreach (Element element in subdomain.ElementsDictionary.Values)
{
if (!(element.ElementType is IPorousFiniteElement))
{
continue;
}
IPorousFiniteElement e = (IPorousFiniteElement)element.ElementType;
IMatrix2D <double> q = e.CouplingMatrix(element);
int iElementMatrixRow = 0;
for (int i = 0; i < element.ElementType.DOFEnumerator.GetDOFTypes(element).Count; i++)
{
Node nodeRow = element.Nodes[i];
foreach (DOFType dofTypeRow in element.ElementType.DOFEnumerator.GetDOFTypes(element)[i])
{
if (dofTypeRow != DOFType.Pore)
{
continue;
}
int dofRow = subdomain.NodalDOFsDictionary[nodeRow.ID][dofTypeRow];
if (dofRow != -1)
{
int iElementMatrixColumn = 0;
for (int j = 0; j < element.ElementType.DOFEnumerator.GetDOFTypes(element).Count; j++)
{
Node nodeColumn = element.Nodes[j];
foreach (DOFType dofTypeColumn in element.ElementType.DOFEnumerator.GetDOFTypes(element)[j])
{
if (dofTypeColumn == DOFType.Pore)
{
continue;
}
int dofColumn = subdomain.NodalDOFsDictionary[nodeColumn.ID][dofTypeColumn];
if (dofColumn != -1)
{
qSubdomain[dofColumn, dofRow] += q[iElementMatrixRow, iElementMatrixColumn];
}
iElementMatrixColumn++;
}
}
}
iElementMatrixRow++;
}
}
}
return(qSubdomain);
}
public void Paint(IDrawspace drawspace)
{
IMatrix2D copyXform = drawspace.Provider.CopyTransform(drawspace.PeekTransform());
copyXform.PreMultiply(LocalXform);
drawspace.PushTransform(copyXform);
drawspace.PushClip(LocalClip);
PaintComponent(drawspace);
drawspace.PopClip();
drawspace.PopTransform();
}
private IMatrix2D <double> PorousMatrix(Element element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <DOFType> dofTypes in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofType in dofTypes)
{
dofs++;
}
}
SymmetricMatrix2D <double> poreMass = new SymmetricMatrix2D <double>(dofs);
IMatrix2D <double> mass = solidMassProvider.Matrix(element);
int matrixRow = 0;
int solidRow = 0;
foreach (IList <DOFType> dofTypesRow in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
foreach (IList <DOFType> dofTypesCol in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == DOFType.Pore)
{
}
else
{
if (dofTypeRow != DOFType.Pore)
{
poreMass[matrixRow, matrixCol] = mass[solidRow, solidCol] * massCoefficient;
}
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow != DOFType.Pore)
{
solidRow++;
}
matrixRow++;
}
}
return(poreMass);
}
public void Draw(VeldridDrawspace dspace, IMatrix2D matrix)
{
dspace.CommandList.SetVertexBuffer(0, Vertices);
dspace.CommandList.SetIndexBuffer(Indices, IndexFormat.UInt16);
dspace.CommandList.SetPipeline(dspace.Pipeline);
// Issue a Draw command for a single instance with 4 indices.
dspace.CommandList.DrawIndexed(
indexCount: 4,
instanceCount: 1,
indexStart: 0,
vertexOffset: 0,
instanceStart: 0);
}
public IMatrix2D <double> Matrix(Element element)
{
if (element.ElementType is IPorousFiniteElement)
{
return(PorousMatrix(element));
}
else
{
IMatrix2D <double> massMatrix = solidMassProvider.Matrix(element);
massMatrix.Scale(massCoefficient);
return(massMatrix);
}
}
public IMatrix2D <double> Matrix(Element element)
{
if (element.ElementType is IPorousFiniteElement)
{
return(PorousMatrix(element));
}
else
{
IMatrix2D <double> dampingMatrix = solidDampingProvider.Matrix(element);
dampingMatrix.Scale(dampingCoefficient);
return(dampingMatrix);
}
}
public double[] CalculateForces(Element element, double[] localDisplacements, double[] localdDisplacements)
{
IMatrix2D <double> stiffnessMatrix = StiffnessMatrix(element);
Vector <double> disps = new Vector <double>(localDisplacements.Length);
double[] forces = new double[localDisplacements.Length];
for (int i = 0; i < localDisplacements.Length; i++)
{
//disps[i] = localDisplacements[i] + localdDisplacements[i];
disps[i] = localDisplacements[i];
}
stiffnessMatrix.Multiply(disps, forces);
return(forces);
}
public IMatrix2D <double> GetTransformedMatrix(IMatrix2D <double> matrix)
{
var e = embeddedElement.ElementType as IEmbeddedElement;
//if (e == null || !isElementEmbedded) return matrix;
if (e == null)
{
return(matrix);
}
if (e.EmbeddedNodes.Count == 0)
{
return(matrix);
}
return(transformationMatrix.Transpose() * ((SymmetricMatrix2D <double>)matrix).ToMatrix2D() * transformationMatrix);
}
private void ComposeStochasticMatrixFromMatrices()
{
var currentRandomNumbers = randomNumbers[currentSimulation];
var coefficients = new double[] { 1 }.Concat(currentRandomNumbers).ToList <double>();
var matricesPerSubdomain = new Dictionary <int, IMatrix2D <double>[]>();
foreach (var subdomain in subdomains.Values)
{
int id = subdomain.ID;
var tempMatrices = new IMatrix2D <double> [expansionOrder + 1];
for (int i = 0; i <= expansionOrder; i++)
{
tempMatrices[i] = matrices[i][id];
}
matricesPerSubdomain.Add(id, tempMatrices);
}
foreach (var subdomain in subdomains.Values)
{
subdomain.Matrix = (SkylineMatrix2D <double>)((SkylineMatrix2D <double>)matrices[0][subdomain.ID]).Clone();
}
foreach (var subdomain in subdomains.Values)
{
subdomain.Matrix.LinearCombination(coefficients, matricesPerSubdomain[subdomain.ID]);
}
//for (int i = 0; i < expansionOrder; i++)
//{
// foreach (var subdomain in subdomains.Values)
// {
// SkylineMatrix2D<double> k = (SkylineMatrix2D<double>)matrices[i + 1][subdomain.ID];
// subdomain.Matrix.LinearCombination(new double[] { randomNumbers[currentSimulation][i] }, new IMatrix2D<double>[] { k });
// }
//}
}
public IMatrix2D CopyTransform(IMatrix2D source)
{
return(new Matrix2D(source));
}
public IMatrix2D <double> GetTransformedMatrix(IMatrix2D <double> matrix)
{
return(matrix);
}
private void CreateElementGaussPoints()
{
GaussLegendrePoint1D[] gaussPointsPerAxisKsi =
GaussQuadrature.GetGaussLegendrePoints(model.DegreeKsi);
GaussLegendrePoint1D[] gaussPointsPerAxisHeta =
GaussQuadrature.GetGaussLegendrePoints(model.DegreeHeta);
IVector <double> coordinatesKsi = new Vector <double>(gaussPointsPerAxisKsi.Length);
IVector <double> weightsKsi = new Vector <double>(gaussPointsPerAxisKsi.Length);
for (int indexKsi = 0; indexKsi < gaussPointsPerAxisKsi.Length; indexKsi++)
{
coordinatesKsi[indexKsi] = 0.5 * (knots[0].Ksi + knots[2].Ksi + (knots[2].Ksi - knots[0].Ksi) * gaussPointsPerAxisKsi[indexKsi].Coordinate);
weightsKsi[indexKsi] = 0.5 * ((knots[2].Ksi - knots[0].Ksi) * gaussPointsPerAxisKsi[indexKsi].WeightFactor);
}
IVector <double> coordinatesHeta = new Vector <double>(gaussPointsPerAxisHeta.Length);
IVector <double> weightsHeta = new Vector <double>(gaussPointsPerAxisHeta.Length);
for (int indexHeta = 0; indexHeta < gaussPointsPerAxisHeta.Length; indexHeta++)
{
coordinatesHeta[indexHeta] = 0.5 * (knots[0].Heta + knots[2].Heta + (knots[2].Heta - knots[0].Heta) * gaussPointsPerAxisHeta[indexHeta].Coordinate);
weightsHeta[indexHeta] = 0.5 * ((knots[2].Heta - knots[0].Heta) * gaussPointsPerAxisHeta[indexHeta].WeightFactor);
}
IList <ControlPoint> controlPointsElement = new List <ControlPoint>();
for (int k = 0; k < (model.DegreeKsi + 1) * (model.DegreeHeta + 1); k++)
{
controlPointsElement.Add(model.ControlPoints[this.connectivity[k]]);
}
ShapeNURBS2D nurbs = new ShapeNURBS2D(this, model, coordinatesKsi, coordinatesHeta, controlPointsElement);
for (int i = 0; i < gaussPointsPerAxisKsi.Length; i++)
{
for (int j = 0; j < gaussPointsPerAxisHeta.Length; j++)
{
IMatrix2D <double> jacobianMatrix = new Matrix2D <double>(2, 2);
for (int k = 0; k < controlPointsElement.Count; k++)
{
jacobianMatrix[0, 0] += nurbs.nurbsDerivativeValuesKsi[k, j] * controlPointsElement[k].X;
jacobianMatrix[0, 1] += nurbs.nurbsDerivativeValuesKsi[k, j] * controlPointsElement[k].Y;
jacobianMatrix[1, 0] += nurbs.nurbsDerivativeValuesHeta[k, j] * controlPointsElement[k].X;
jacobianMatrix[1, 1] += nurbs.nurbsDerivativeValuesHeta[k, j] * controlPointsElement[k].Y;
}
double jacdet = jacobianMatrix[0, 0] * jacobianMatrix[1, 1]
- jacobianMatrix[1, 0] * jacobianMatrix[0, 1];
Matrix2D <double> B1 = new Matrix2D <double>(3, 4);
B1[0, 0] += jacobianMatrix[1, 1] / jacdet;
B1[0, 1] += -jacobianMatrix[0, 1] / jacdet;
B1[1, 2] += -jacobianMatrix[1, 0] / jacdet;
B1[1, 3] += jacobianMatrix[0, 0] / jacdet;
B1[2, 0] += -jacobianMatrix[1, 0] / jacdet;
B1[2, 1] += jacobianMatrix[0, 0] / jacdet;
B1[2, 2] += jacobianMatrix[1, 1] / jacdet;
B1[2, 3] += -jacobianMatrix[0, 1] / jacdet;
Matrix2D <double> B2 = new Matrix2D <double>(4, 2 * controlPointsElement.Count);
for (int column = 0; column < 2 * controlPointsElement.Count; column += 2)
{
B2[0, column] += nurbs.nurbsDerivativeValuesKsi[column / 2, j];
B2[1, column] += nurbs.nurbsDerivativeValuesHeta[column / 2, j];
B2[2, column + 1] += nurbs.nurbsDerivativeValuesKsi[column / 2, j];
B2[3, column + 1] += nurbs.nurbsDerivativeValuesHeta[column / 2, j];
}
IMatrix2D <double> B = B1 * B2;
double weightFactor = gaussPointsPerAxisKsi[i].WeightFactor * gaussPointsPerAxisHeta[i].WeightFactor * jacdet;
this.gaussPoints.Add(new GaussLegendrePoint3D(gaussPointsPerAxisKsi[i].Coordinate, gaussPointsPerAxisHeta[j].Coordinate, 0.0, B, weightFactor));
}
}
}
private IMatrix2D <double> PorousMatrix(Element element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <DOFType> dofTypes in elementType.DOFTypes)
{
foreach (DOFType dofType in dofTypes)
{
dofs++;
}
}
SymmetricMatrix2D <double> poreStiffness = new SymmetricMatrix2D <double>(dofs);
for (int i = 0; i < dofs; i++)
{
poreStiffness[i, i] = 1;
}
IMatrix2D <double> permeability = elementType.PermeabilityMatrix(element);
int matrixRow = 0;
int solidRow = 0;
int fluidRow = 0;
foreach (IList <DOFType> dofTypesRow in elementType.DOFTypes)
{
foreach (DOFType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
int fluidCol = 0;
foreach (IList <DOFType> dofTypesCol in elementType.DOFTypes)
{
foreach (DOFType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == DOFType.Pore)
{
if (dofTypeRow == DOFType.Pore)
{
poreStiffness[matrixRow, matrixCol] = permeability[fluidRow, fluidCol];
}
fluidCol++;
}
else
{
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow == DOFType.Pore)
{
fluidRow++;
}
else
{
solidRow++;
}
matrixRow++;
}
}
return(poreStiffness);
}
public ShapeNURBS3D(NURBSElement3D element, IGAModel model, IVector <double> parametricCoordinateKsi, IVector <double> parametricCoordinateHeta, IVector <double> parametricCoordinateZeta, IList <ControlPoint> controlPoints)
{
int numberOfCPHeta = model.KnotValueVectorHeta.Length - model.DegreeHeta - 1;
int numberOfCPZeta = model.KnotValueVectorZeta.Length - model.DegreeZeta - 1;
BSPLines1D bsplinesKsi = new BSPLines1D(model.DegreeKsi, model.KnotValueVectorKsi, parametricCoordinateKsi);
BSPLines1D bsplinesHeta = new BSPLines1D(model.DegreeHeta, model.KnotValueVectorHeta, parametricCoordinateHeta);
BSPLines1D bsplinesZeta = new BSPLines1D(model.DegreeZeta, model.KnotValueVectorZeta, parametricCoordinateZeta);
nurbsValues = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesKsi = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesHeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesZeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
int supportKsi = model.DegreeKsi + 1;
int supportHeta = model.DegreeHeta + 1;
int supportZeta = model.DegreeZeta + 1;
int numberOfElementGaussPoints = (model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
for (int k = 0; k < supportZeta; k++)
{
double sumKsiHetaZeta = 0;
double sumdKsiHetaZeta = 0;
double sumKsidHetaZeta = 0;
double sumKsiHetadZeta = 0;
for (int m = 0; m < numberOfElementGaussPoints; m++)
{
int indexKsi = element.connectivity[m] / (numberOfCPHeta * numberOfCPZeta);
int indexHeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) / numberOfCPZeta;
int indexZeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) % numberOfCPZeta;
sumKsiHetaZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumdKsiHetaZeta += bsplinesKsi.BSPLDerivativeValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumKsidHetaZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLDerivativeValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumKsiHetadZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLDerivativeValues[indexZeta, k] *
controlPoints[m].Weight;
}
for (int m = 0; m < numberOfElementGaussPoints; m++)
{
int indexKsi = element.connectivity[m] / (numberOfCPHeta * numberOfCPZeta);
int indexHeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) / numberOfCPZeta;
int indexZeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) % numberOfCPZeta;
nurbsValues[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / sumKsiHetaZeta;
nurbsDerivativeValuesKsi[m, i *supportHeta *supportZeta + j * supportZeta + k] =
(bsplinesKsi.BSPLDerivativeValues[indexKsi, i] * sumKsiHetaZeta -
bsplinesKsi.BSPLValues[indexKsi, i] * sumdKsiHetaZeta) *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
nurbsDerivativeValuesHeta[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
(bsplinesHeta.BSPLDerivativeValues[indexHeta, j] * sumKsiHetaZeta -
bsplinesHeta.BSPLValues[indexHeta, j] * sumKsidHetaZeta) *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
nurbsDerivativeValuesZeta[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
(bsplinesZeta.BSPLDerivativeValues[indexZeta, k] * sumKsiHetaZeta -
bsplinesZeta.BSPLValues[indexZeta, k] * sumKsiHetadZeta) *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
}
}
}
}
}
private IMatrix2D <double> PorousMatrix(Element element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <DOFType> dofTypes in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofType in dofTypes)
{
dofs++;
}
}
SymmetricMatrix2D <double> poreStiffness = new SymmetricMatrix2D <double>(dofs);
IMatrix2D <double> stiffness = solidStiffnessProvider.Matrix(element);
IMatrix2D <double> permeability = elementType.PermeabilityMatrix(element);
int matrixRow = 0;
int solidRow = 0;
int fluidRow = 0;
foreach (IList <DOFType> dofTypesRow in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
int fluidCol = 0;
foreach (IList <DOFType> dofTypesCol in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == DOFType.Pore)
{
if (dofTypeRow == DOFType.Pore)
{
// H correction
poreStiffness[matrixRow, matrixCol] = -permeability[fluidRow, fluidCol];
}
//poreStiffness[matrixRow, matrixCol] = permeability[fluidRow, fluidCol];
fluidCol++;
}
else
{
if (dofTypeRow != DOFType.Pore)
{
poreStiffness[matrixRow, matrixCol] = stiffness[solidRow, solidCol] * stiffnessCoefficient;
}
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow == DOFType.Pore)
{
fluidRow++;
}
else
{
solidRow++;
}
matrixRow++;
}
}
return(poreStiffness);
}
public BSPLines1D(int degree, IVector <double> knotValueVector, IVector <double> parametricCoordinates)
{
if (degree <= 0)
{
throw new IndexOutOfRangeException("The degree must be greater or equal to zero");
}
else if (knotValueVector == null)
{
throw new ArgumentNullException("Knot Value Vector is null");
}
int order = degree + 1;
int numberOfCP = knotValueVector.Length - order;
int numberOfGP = parametricCoordinates.Length;
BSPLValues = new Matrix2D <double>(numberOfCP + degree, numberOfGP);
BSPLDerivativeValues = new Matrix2D <double>(numberOfCP + degree, numberOfGP);
// BSPLine Basis Functions. Degree=0.
for (int i = 0; i < numberOfGP; i++)
{
for (int j = 0; j < numberOfCP; j++)
{
if (knotValueVector[j] <= parametricCoordinates[i] && parametricCoordinates[i] < knotValueVector[j + 1])
{
BSPLValues[j, i] = 1;
}
else
{
BSPLValues[j, i] = 0;
}
}
}
// BSPLineBasis Basis Functions. Degree=1:p
for (int i = 0; i < degree; i++)
{
for (int j = 0; j < numberOfCP + degree - i; j++)
{
for (int k = 0; k < numberOfGP; k++)
{
double additive1 = 0;
double additive2 = 0;
double additiveDerivative1 = 0;
double additiveDerivative2 = 0;
double denominator1 = knotValueVector[j + i] - knotValueVector[j];
double denominator2 = knotValueVector[j + i + 1] - knotValueVector[j + 1];
if (denominator1 != 0)
{
additive1 = (parametricCoordinates[k] - knotValueVector[j]) / denominator1 * BSPLValues[j, k];
additiveDerivative1 = ((parametricCoordinates[k] - knotValueVector[j]) * BSPLDerivativeValues[j, k]
+ BSPLValues[j, k]) / denominator1;
}
if (denominator2 != 0)
{
additive2 = (knotValueVector[j + i + 1] - parametricCoordinates[k]) / denominator2 * BSPLValues[j + 1, k];
additiveDerivative2 = ((knotValueVector[j + i + 1] - parametricCoordinates[k]) * BSPLDerivativeValues[j + 1, k] - BSPLValues[j + 1, k]) / denominator2;
}
BSPLValues[j, k] = additive1 + additive2;
BSPLDerivativeValues[j, k] = additiveDerivative1 + additiveDerivative2;
}
}
}
}
public void PreMultiply(IMatrix2D lhs)
{
SKMatrix.PreConcat(ref _skMatrix, ((Matrix2D)lhs)._skMatrix);
}
internal SKMatrix _skMatrix; // a strut
public Matrix2D(IMatrix2D source)
{
_skMatrix = ((Matrix2D)source)._skMatrix; // copy on assign because struct
}
private IMatrix2D <double> PorousMatrix(Element element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <DOFType> dofTypes in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofType in dofTypes)
{
dofs++;
}
}
SymmetricMatrix2D <double> poreDamping = new SymmetricMatrix2D <double>(dofs);
IMatrix2D <double> damping = solidDampingProvider.Matrix(element);
IMatrix2D <double> saturation = elementType.SaturationMatrix(element);
IMatrix2D <double> coupling = elementType.CouplingMatrix(element);
int matrixRow = 0;
int solidRow = 0;
int fluidRow = 0;
foreach (IList <DOFType> dofTypesRow in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
int fluidCol = 0;
foreach (IList <DOFType> dofTypesCol in elementType.DOFEnumerator.GetDOFTypes(element))
{
foreach (DOFType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == DOFType.Pore)
{
if (dofTypeRow == DOFType.Pore)
{
poreDamping[matrixRow, matrixCol] = -saturation[fluidRow, fluidCol];
}
else
{
poreDamping[matrixRow, matrixCol] = coupling[fluidCol, solidRow];
}
fluidCol++;
}
else
{
if (dofTypeRow != DOFType.Pore)
{
poreDamping[matrixRow, matrixCol] = damping[solidRow, solidCol] * dampingCoefficient;
}
else
{
poreDamping[matrixRow, matrixCol] = coupling[fluidRow, solidCol];
}
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow == DOFType.Pore)
{
fluidRow++;
}
else
{
solidRow++;
}
matrixRow++;
}
}
return(poreDamping);
}
