protected override void ComputeValues(NodeSet NS, int j0, int Len, MultidimensionalArray output)
{
MultidimensionalArray Phi = m_owner.GetLevSetValues(NS, j0, Len);
MultidimensionalArray GradPhi = m_owner.GetLevelSetReferenceGradients(NS, j0, Len);
MultidimensionalArray HessPhi = m_owner.GetLevelSetReferenceHessian(NS, j0, Len);
MultidimensionalArray ooNormGrad = new MultidimensionalArray(2);
MultidimensionalArray Laplace = new MultidimensionalArray(2);
MultidimensionalArray Q = new MultidimensionalArray(3);
int K = output.GetLength(1);
int D = GradPhi.GetLength(2);
Debug.Assert(D == this.m_owner.m_owner.GridDat.SpatialDimension);
ooNormGrad.Allocate(Len, K);
Laplace.Allocate(Len, K);
Q.Allocate(Len, K, D);
// compute the monstrous formula
// -----------------------------
// norm of Gradient:
for (int d = 0; d < D; d++)
{
var GradPhi_d = GradPhi.ExtractSubArrayShallow(-1, -1, d);
ooNormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
ooNormGrad.ApplyAll(x => 1.0 / Math.Sqrt(x));
// laplacian of phi:
for (int d = 0; d < D; d++)
{
var HessPhi_d_d = HessPhi.ExtractSubArrayShallow(-1, -1, d, d);
Laplace.Acc(1.0, HessPhi_d_d);
}
// result = Laplacian(phi)/|Grad phi|
output.Multiply(1.0, Laplace, ooNormGrad, 0.0, "ik", "ik", "ik");
// result = Grad(1/|Grad(phi)|)
for (int d1 = 0; d1 < D; d1++)
{
var Qd = Q.ExtractSubArrayShallow(-1, -1, d1);
for (int d2 = 0; d2 < D; d2++)
{
var Grad_d2 = GradPhi.ExtractSubArrayShallow(-1, -1, d2);
var Hess_d2_d1 = HessPhi.ExtractSubArrayShallow(-1, -1, d2, d1);
Qd.Multiply(-1.0, Grad_d2, Hess_d2_d1, 1.0, "ik", "ik", "ik");
}
}
ooNormGrad.ApplyAll(x => x * x * x);
output.Multiply(1.0, GradPhi, Q, ooNormGrad, 1.0, "ik", "ikd", "ikd", "ik");
}
/// <summary>
/// Constructs a new flux builder.
/// </summary>
/// <param name="control"></param>
/// <param name="boundaryMap"></param>
/// <param name="speciesMap"></param>
/// <param name="gridData"></param>
public OptimizedSIPGFluxBuilder(CNSControl control, IBoundaryConditionMap boundaryMap, ISpeciesMap speciesMap, GridData gridData)
: base(control, boundaryMap, speciesMap)
{
this.gridData = gridData;
//Create Functions for calculation the cell metric, needed as Func<> because
//LevelSet field and HMF options are not known at this point
if (speciesMap is IBM.ImmersedSpeciesMap)
{
// IBM case
ImmersedSpeciesMap IBMspeciesMap = speciesMap as ImmersedSpeciesMap;
cellMetricFunc = delegate() {
SpeciesId species = IBMspeciesMap.Tracker.GetSpeciesId(IBMspeciesMap.Control.FluidSpeciesName);
MultidimensionalArray cellMetric = IBMspeciesMap.CellAgglomeration.CellLengthScales[species].CloneAs();
cellMetric.ApplyAll(x => 1 / x);
// Needed, because 1/x produces NaN in void cells and can happen that penalty factor leads then to NaN
cellMetric.ApplyAll(delegate(double x) {
if (double.IsNaN(x) || double.IsInfinity(x))
{
return(0);
}
else
{
return(x);
}
});
return(cellMetric);
};
}
else
{
// Non-IBM
cellMetricFunc = () => gridData.Cells.cj;
}
}
internal void Tf(int j0, int Len, NodeSet N, MultidimensionalArray result)
{
f(j0, Len, N, result);
Debug.Assert(Len == result.GetLength(0));
Debug.Assert(result.Dimension == 2);
result.ApplyAll(this.T);
}
/// <summary>
/// First order approximation of delta >= sup_x|psi(x) - psi(x_center)|
/// </summary>
/// <param name="Arg"></param>
/// <param name="psi"></param>
/// <param name="x_center"></param>
/// <param name="cell"></param>
/// <returns></returns>
protected override double EvaluateBounds(LinearSayeSpace <Cube> Arg, LinearPSI <Cube> psi, NodeSet x_center, int cell)
{
double[] arr = new double[RefElement.SpatialDimension];
Arg.Diameters.CopyTo(arr, 0);
psi.SetInactiveDimsToZero(arr);
MultidimensionalArray diameters = MultidimensionalArray.CreateWrapper(arr, 3);
NodeSet nodeOnPsi = psi.ProjectOnto(x_center);
MultidimensionalArray grad = ReferenceGradient(nodeOnPsi, cell);
grad.ApplyAll(x => Math.Abs(x));
double delta = grad.InnerProduct(diameters);
return(delta);
}
protected override bool HeightDirectionIsSuitable(SayeSquare arg, LinearPSI <Square> psi, NodeSet x_center,
int heightDirection, MultidimensionalArray gradient, int cell)
{
//Determine bounds
//-----------------------------------------------------------------------------------------------------------------
double[] arr = arg.Diameters;
psi.SetInactiveDimsToZero(arr);
MultidimensionalArray diameters = MultidimensionalArray.CreateWrapper(arr, new int[] { 2, 1 });
NodeSet nodeOnPsi = psi.ProjectOnto(x_center);
MultidimensionalArray hessian = lsData.GetLevelSetReferenceHessian(nodeOnPsi, cell, 1);
hessian = hessian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 });
MultidimensionalArray jacobian = grid.InverseJacobian.GetValue_Cell(nodeOnPsi, cell, 1);
jacobian = jacobian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 });
hessian = jacobian * hessian;
hessian.ApplyAll(x => Math.Abs(x));
//abs(Hessian) * diameters = delta
MultidimensionalArray delta = hessian * diameters;
delta = delta.ExtractSubArrayShallow(new int[] { -1, 0 });
//Check if suitable
//-----------------------------------------------------------------------------------------------------------------
//|gk| > δk
if (Math.Abs(gradient[heightDirection]) > delta[heightDirection])
{
bool suitable = true;
// Sum_j( g_j + delta_j)^2 / (g_k - delta_k)^2 < 20
double sum = 0;
for (int j = 0; j < delta.Length; ++j)
{
sum += Math.Pow(gradient[j] + delta[j], 2);
}
sum /= Math.Pow(gradient[heightDirection] - delta[heightDirection], 2);
suitable &= sum < 20;
return(suitable);
}
return(false);
}
/// <summary>
/// First order approximation of delta >= sup_x|psi(x) - psi(x_center)|
/// </summary>
/// <param name="Arg"></param>
/// <param name="psi"></param>
/// <param name="x_center"></param>
/// <param name="cell"></param>
/// <returns></returns>
protected override double EvaluateBounds(SayeSquare Arg, LinearPSI <Square> psi, NodeSet x_center, int cell)
{
double[] arr = new double[Arg.Dimension];
Arg.Diameters.CopyTo(arr, 0);
psi.SetInactiveDimsToZero(arr);
MultidimensionalArray diameters = MultidimensionalArray.CreateWrapper(arr, new int[] { 2 });
NodeSet nodeOnPsi = psi.ProjectOnto(x_center);
MultidimensionalArray grad = ScaledReferenceGradient(nodeOnPsi, cell);
grad.ApplyAll(x => Math.Abs(x));
double delta = grad.InnerProduct(diameters) * sqrt_2;
return(delta);
}
/// <summary>
/// curvature computation according to Bonnet's formula
/// Copy-Paste from <see cref="LevelSet.EvaluatetotalCurvature"/>, since there is no analytic formula for the curvature of an ellipse
/// </summary>
public void EvaluateTotalCurvature(int j0, int Len, NodeSet NodeSet, MultidimensionalArray result)
{
// (siehe FK, persoenliche Notizen, 08mar13)
// checks
// ------
int K = NodeSet.NoOfNodes;
if (result.Dimension != 2)
{
throw new ArgumentException();
}
if (result.GetLength(0) != Len)
{
throw new ArgumentException();
}
if (result.GetLength(1) != K)
{
throw new ArgumentException();
}
int D = NodeSet.SpatialDimension;
//Debug.Assert(D == this.GridDat.SpatialDimension);
// buffers:
// --------
//MultidimensionalArray Phi = new MultidimensionalArray(2);
MultidimensionalArray GradPhi = new MultidimensionalArray(3);
MultidimensionalArray HessPhi = new MultidimensionalArray(4);
MultidimensionalArray ooNormGrad = new MultidimensionalArray(2);
MultidimensionalArray Laplace = new MultidimensionalArray(2);
MultidimensionalArray Q = new MultidimensionalArray(3);
//Phi.Allocate(Len, K);
GradPhi.Allocate(Len, K, D);
HessPhi.Allocate(Len, K, D, D);
ooNormGrad.Allocate(Len, K);
Laplace.Allocate(Len, K);
Q.Allocate(Len, K, D);
// derivatives
// -----------
// evaluate gradient
this.EvaluateGradient(j0, Len, NodeSet, GradPhi);
// evaluate Hessian
this.EvaluateHessian(j0, Len, NodeSet, HessPhi);
// compute the monstrous formula
// -----------------------------
// norm of Gradient:
for (int d = 0; d < D; d++)
{
var GradPhi_d = GradPhi.ExtractSubArrayShallow(-1, -1, d);
ooNormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
ooNormGrad.ApplyAll(x => 1.0 / Math.Sqrt(x));
// laplacian of phi:
for (int d = 0; d < D; d++)
{
var HessPhi_d_d = HessPhi.ExtractSubArrayShallow(-1, -1, d, d);
Laplace.Acc(1.0, HessPhi_d_d);
}
// result = Laplacian(phi)/|Grad phi|
result.Multiply(1.0, Laplace, ooNormGrad, 0.0, "ik", "ik", "ik");
// result += Grad(1/|Grad(phi)|)
for (int d1 = 0; d1 < D; d1++)
{
var Qd = Q.ExtractSubArrayShallow(-1, -1, d1);
for (int d2 = 0; d2 < D; d2++)
{
var Grad_d2 = GradPhi.ExtractSubArrayShallow(-1, -1, d2);
var Hess_d2_d1 = HessPhi.ExtractSubArrayShallow(-1, -1, d2, d1);
Qd.Multiply(-1.0, Grad_d2, Hess_d2_d1, 1.0, "ik", "ik", "ik");
}
}
ooNormGrad.ApplyAll(x => x * x * x);
result.Multiply(1.0, GradPhi, Q, ooNormGrad, 1.0, "ik", "ikd", "ikd", "ik");
}
/// <summary>
/// Computation of mean curvature according to Bonnet's formula.
/// </summary>
/// <param name="scale"></param>
/// <param name="Output">
/// output.
/// </param>
/// <param name="quadScheme"></param>
/// <param name="UseCenDiffUpTo">
/// Either 0, 1, or 2:
/// If 0, all derivatives are computed locally (broken derivative);
/// if 1, the first order derivatives are computed by central
/// differences, while the second order ones are computed locally,
/// based on the first order ones;
/// if 2, all derivatives are computed by central differences.
/// </param>
/// <param name="_1stDerivDegree">
/// Relative DG polynomial degree for the 1st order derivatives, i.e.
/// degree is <paramref name="_1stDerivDegree"/>+<em>p</em>, where
/// <em>p</em> is the degree of this field.
/// Only active if <paramref name="UseCenDiffUpTo"/> is greater than 0.
/// </param>
/// <param name="_2ndDerivDegree">
/// Relative DG polynomial degree for the 2nd order derivatives, i.e.
/// degree is <paramref name="_2ndDerivDegree"/>+<em>p</em>, where
/// <em>p</em> is the degree of this field. Only active if
/// <paramref name="UseCenDiffUpTo"/> is greater than 1.
/// </param>
/// <remarks>
/// using central differences causes memory allocation: <em>D</em>
/// fields for <paramref name="UseCenDiffUpTo"/>=1, and
/// <em>D</em>*(<em>D</em>+1) for <paramref name="UseCenDiffUpTo"/>=2,
/// where <em>D</em> notates the spatial dimension.
/// </remarks>
public void ProjectTotalcurvature2(
double scale,
SinglePhaseField Output,
int UseCenDiffUpTo,
int _1stDerivDegree = 0,
int _2ndDerivDegree = 0,
CellQuadratureScheme quadScheme = null)
{
using (new FuncTrace()) {
if (UseCenDiffUpTo < 0 || UseCenDiffUpTo > 2)
{
throw new ArgumentOutOfRangeException();
}
//int M = Output.Basis.Length;
//int N = this.Basis.Length;
int D = this.GridDat.SpatialDimension;
//var NSC = m_context.NSC;
SubGrid sgrd = null;
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.InnerEdge;
if (UseCenDiffUpTo >= 1 && quadScheme != null && quadScheme.Domain != null)
{
sgrd = new SubGrid(quadScheme.Domain);
bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary;
}
// compute 1st order derivatives by central differences, if desired
// ================================================================
Basis B2 = new Basis(this.GridDat, this.Basis.Degree + _1stDerivDegree);
SinglePhaseField[] GradientVector = null;
if (UseCenDiffUpTo >= 1)
{
GradientVector = new SinglePhaseField[D];
for (int d = 0; d < D; d++)
{
GradientVector[d] = new SinglePhaseField(B2);
GradientVector[d].DerivativeByFlux(1.0, this, d, sgrd, bndMode);
}
}
// compute 2nd order derivatives by central differences, if desired
// ===============================================================
Basis B3 = new Basis(this.GridDat, this.Basis.Degree + _2ndDerivDegree);
SinglePhaseField[,] HessianTensor = null;
if (UseCenDiffUpTo >= 2)
{
HessianTensor = new SinglePhaseField[D, D];
for (int d1 = 0; d1 < D; d1++)
{
for (int d2 = 0; d2 < D; d2++)
{
HessianTensor[d1, d2] = new SinglePhaseField(B3);
HessianTensor[d1, d2].DerivativeByFlux(1.0, GradientVector[d1], d2, sgrd, bndMode);
}
}
}
// compute and project
// ===================
// buffers:
MultidimensionalArray Phi = new MultidimensionalArray(2);
MultidimensionalArray GradPhi = new MultidimensionalArray(3);
MultidimensionalArray HessPhi = new MultidimensionalArray(4);
MultidimensionalArray ooNormGrad = new MultidimensionalArray(2);
MultidimensionalArray Laplace = new MultidimensionalArray(2);
MultidimensionalArray Q = new MultidimensionalArray(3);
// evaluate/project:
//double Erracc = 0;
Output.ProjectField(scale,
(ScalarFunctionEx) delegate(int j0, int Len, NodeSet NodeSet, MultidimensionalArray result) { // ScalarFunction2
Debug.Assert(result.Dimension == 2);
Debug.Assert(Len == result.GetLength(0));
int K = result.GetLength(1); // number of nodes
// alloc buffers
// -------------
if (Phi.GetLength(0) != Len || Phi.GetLength(1) != K)
{
Phi.Allocate(Len, K);
GradPhi.Allocate(Len, K, D);
HessPhi.Allocate(Len, K, D, D);
ooNormGrad.Allocate(Len, K);
Laplace.Allocate(Len, K);
Q.Allocate(Len, K, D);
}
else
{
Phi.Clear();
GradPhi.Clear();
HessPhi.Clear();
ooNormGrad.Clear();
Laplace.Clear();
Q.Clear();
}
// evaluate Gradient and Hessian
// -----------------------------
if (UseCenDiffUpTo >= 1)
{
for (int d = 0; d < D; d++)
{
GradientVector[d].Evaluate(j0, Len, NodeSet, GradPhi.ExtractSubArrayShallow(-1, -1, d));
}
}
else
{
this.EvaluateGradient(j0, Len, NodeSet, GradPhi);
}
if (UseCenDiffUpTo == 2)
{
for (int d1 = 0; d1 < D; d1++)
{
for (int d2 = 0; d2 < D; d2++)
{
HessianTensor[d1, d2].Evaluate(j0, Len, NodeSet, HessPhi.ExtractSubArrayShallow(-1, -1, d1, d2));
}
}
}
else if (UseCenDiffUpTo == 1)
{
for (int d = 0; d < D; d++)
{
var GradientVector_d = GradientVector[d];
GradientVector_d.EvaluateGradient(j0, Len, NodeSet, HessPhi.ExtractSubArrayShallow(-1, -1, d, -1), 0, 0.0);
}
}
else if (UseCenDiffUpTo == 0)
{
this.EvaluateHessian(j0, Len, NodeSet, HessPhi);
}
else
{
Debug.Assert(false);
}
// compute the monstrous formula
// -----------------------------
// norm of Gradient:
for (int d = 0; d < D; d++)
{
var GradPhi_d = GradPhi.ExtractSubArrayShallow(-1, -1, d);
ooNormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
ooNormGrad.ApplyAll(x => 1.0 / Math.Sqrt(x));
// laplacian of phi:
for (int d = 0; d < D; d++)
{
var HessPhi_d_d = HessPhi.ExtractSubArrayShallow(-1, -1, d, d);
Laplace.Acc(1.0, HessPhi_d_d);
}
// result = Laplacian(phi)/|Grad phi|
result.Multiply(1.0, Laplace, ooNormGrad, 0.0, "ik", "ik", "ik");
// result = Grad(1/|Grad(phi)|)
for (int d1 = 0; d1 < D; d1++)
{
var Qd = Q.ExtractSubArrayShallow(-1, -1, d1);
for (int d2 = 0; d2 < D; d2++)
{
var Grad_d2 = GradPhi.ExtractSubArrayShallow(-1, -1, d2);
var Hess_d2_d1 = HessPhi.ExtractSubArrayShallow(-1, -1, d2, d1);
Qd.Multiply(-1.0, Grad_d2, Hess_d2_d1, 1.0, "ik", "ik", "ik");
}
}
ooNormGrad.ApplyAll(x => x * x * x);
result.Multiply(1.0, GradPhi, Q, ooNormGrad, 1.0, "ik", "ikd", "ikd", "ik");
//for (int i = 0; i < Len; i++) {
// for (int k = 0; k < K; k++) {
// double acc = 0;
// for (int d = 0; d < D; d++) {
// acc += GradPhi[i,k,d]*Q[i,k,d]*ooNormGrad[i,k];
// }
// Erracc += (acc - result[i,k]).Abs();
// }
//}
},
quadScheme.SaveCompile(this.GridDat, (Output.Basis.Degree + this.m_Basis.Degree * (this.m_Basis.Degree - 1) * D) * 2)
);
}
}
public void WriteTrendToTable(bool ErrorOrResidual, bool SepPoly, bool SepLev, out string[] Titels, out MultidimensionalArray ConvTrendData)
{
Dictionary <Tuple <int, int, int>, List <double> > data = ErrorOrResidual ? ErrNormTrend : ResNormTrend;
List <string> titleS = new List <string>();
int iCol = 0;
Dictionary <Tuple <int, int, int>, int> ColumnIndex = new Dictionary <Tuple <int, int, int>, int>();
foreach (var kv in data)
{
int iLevel = kv.Key.Item1;
int pDG = kv.Key.Item3;
int iVar = kv.Key.Item2;
string title;
if (SepPoly == false && SepLev == false)
{
title = string.Format("(var#{0})", iVar);
}
else if (SepPoly == false && SepLev == true)
{
title = string.Format("(var#{0},mg.lev.{1})", iVar, iLevel);
}
else if (SepPoly == true && SepLev == false)
{
title = string.Format("(var#{0},p={2})", iVar, pDG);
}
else if (SepPoly == true && SepLev == true)
{
title = string.Format("(var#{0},mg.lev.{1},p={2})", iVar, iLevel, pDG);
}
else
{
throw new ApplicationException();
}
int iColKv = titleS.IndexOf(title);
if (iColKv < 0)
{
titleS.Add(title);
iColKv = iCol;
iCol++;
}
ColumnIndex.Add(kv.Key, iColKv);
}
Titels = titleS.ToArray();
ConvTrendData = MultidimensionalArray.Create(data.First().Value.Count, titleS.Count);
foreach (var kv in data)
{
double[] Column = kv.Value.ToArray();
for (int l = 0; l < Column.Length; l++)
{
Column[l] = Column[l].Pow2();
}
if (ConvTrendData.GetLength(0) != Column.Length)
{
throw new ApplicationException();
}
int iColkv = ColumnIndex[kv.Key];
ConvTrendData.ExtractSubArrayShallow(-1, iColkv).AccVector(1.0, Column);
}
ConvTrendData.ApplyAll(x => Math.Sqrt(x));
}
private double[] ComputeBenchmarkQuantities()
{
int order = 0;
if (CorrectionLsTrk.GetCachedOrders().Count > 0)
{
order = CorrectionLsTrk.GetCachedOrders().Max();
}
else
{
order = 1;
}
var SchemeHelper = CorrectionLsTrk.GetXDGSpaceMetrics(CorrectionLsTrk.SpeciesIdS.ToArray(), order, 1).XQuadSchemeHelper;
// area of bubble
double area = 0.0;
SpeciesId spcId = CorrectionLsTrk.SpeciesIdS[1];
var vqs = SchemeHelper.GetVolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
vqs.Compile(CorrectionLsTrk.GridDat, order),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
area += ResultsOfIntegration[i, 0];
}
}
).Execute();
area = area.MPISum();
// surface
double surface = 0.0;
//CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
var surfElemVol = SchemeHelper.Get_SurfaceElement_VolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
surfElemVol.Compile(CorrectionLsTrk.GridDat, this.m_HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
surface += ResultsOfIntegration[i, 0];
}
}
).Execute();
surface = surface.MPISum();
// circularity
double diamtr_c = Math.Sqrt(4 * area / Math.PI);
double perimtr_b = surface;
double circ = Math.PI * diamtr_c / perimtr_b;
// total concentration, careful above values are "old" when CorrectionTracker is not updated, this value is always "new"
double concentration = 0.0;
var tqs = new CellQuadratureScheme();
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
tqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
phi.Evaluate(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
concentration += ResultsOfIntegration[i, 0];
}
}
).Execute();
concentration = concentration.MPISum();
// total mixing energy
double energy = 0.0;
var eqs = new CellQuadratureScheme();
int D = phi.GridDat.SpatialDimension;
SinglePhaseField[] PhiGrad = new SinglePhaseField[D];
for (int d = 0; d < D; d++)
{
PhiGrad[d] = new SinglePhaseField(phi.Basis, string.Format("G_{0}", d));
PhiGrad[d].Derivative(1.0, phi, d);
}
MultidimensionalArray _Phi = new MultidimensionalArray(2);
MultidimensionalArray _GradPhi = new MultidimensionalArray(3);
MultidimensionalArray _NormGrad = new MultidimensionalArray(2);
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
eqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
int K = EvalResult.GetLength(1);
// alloc buffers
// -------------
if (_Phi.GetLength(0) != Length || _Phi.GetLength(1) != K)
{
_Phi.Allocate(Length, K);
_GradPhi.Allocate(Length, K, D);
_NormGrad.Allocate(Length, K);
}
else
{
_Phi.Clear();
_GradPhi.Clear();
_NormGrad.Clear();
}
// chemical potential
phi.Evaluate(i0, Length, QR.Nodes, _Phi.ExtractSubArrayShallow(-1, -1));
_Phi.ApplyAll(x => 0.25 / (this.Control.cahn.Pow2()) * (x.Pow2() - 1.0).Pow2());
for (int d = 0; d < D; d++)
{
PhiGrad[d].Evaluate(i0, Length, QR.Nodes, _GradPhi.ExtractSubArrayShallow(-1, -1, d));
}
// free surface energy
for (int d = 0; d < D; d++)
{
var GradPhi_d = _GradPhi.ExtractSubArrayShallow(-1, -1, d);
_NormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
_NormGrad.ApplyAll(x => 0.5 * x);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _Phi);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _NormGrad);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
energy += ResultsOfIntegration[i, 0];
}
}
).Execute();
energy = energy.MPISum();
// replace 1.96 (RB_TC2) with actual surface tension
// see Yue (2004)
double lambda = this.Control.cahn.Pow2() * 1.96 * surface / energy;
return(new double[] { area, surface, circ, concentration, energy, lambda, this.Control.diff });
}
/// <summary>
/// provides data collected during a solver run in tabular form
/// </summary>
/// <param name="ErrorOrResidual">
/// - true: output is error against exact solution (if provided) during each iteration
/// - false: output is residual against exact solution (if provided) during each iteration
/// </param>
/// <param name="SepVars">
/// - true: separate column for each variable
/// - false: l2-norm over all variables
/// </param>
/// <param name="SepPoly">
/// - true: separate column for each polynomial degree
/// - false: l2-norm over all polynomial degrees
/// </param>
/// <param name="SepLev">
/// - true: separate column for each multi-grid level
/// - false: l2-norm over all multi-grid levels
/// </param>
/// <param name="Titels">
/// Column names/titles
/// </param>
/// <param name="ConvTrendData">
/// data table:
/// - columns: correspond to <paramref name="Titels"/>
/// - rows: solver iterations
/// </param>
public void WriteTrendToTable(bool ErrorOrResidual, bool SepVars, bool SepPoly, bool SepLev, out string[] Titels, out MultidimensionalArray ConvTrendData)
{
var data = ErrorOrResidual ? ErrNormTrend : ResNormTrend;
List <string> titleS = new List <string>();
int iCol = 0;
Dictionary <(int MGlevel, int iVar, int deg), int> ColumnIndex = new Dictionary <(int, int, int), int>();
foreach (var kv in data)
{
int iLevel = kv.Key.Item1;
int pDG = kv.Key.Item3;
int iVar = kv.Key.Item2;
string title;
{
if (SepVars)
{
title = $"Var{iVar}";
}
else
{
title = "";
}
if (SepLev)
{
if (title.Length > 0)
{
title = title + ",";
}
title = title + $"Mglv{iLevel}";
}
if (SepPoly)
{
if (title.Length > 0)
{
title = title + ",";
}
title = title + $"p={pDG}";
}
if (title.Length > 0)
{
title = "_" + title;
}
if (ErrorOrResidual)
{
title = "Err" + title;
}
else
{
title = "Res" + title;
}
}
/*
* if (SepPoly == false && SepLev == false) {
* title = string.Format("(var#{0})", iVar);
* } else if (SepPoly == false && SepLev == true) {
* title = string.Format("(var#{0},mg.lev.{1})", iVar, iLevel);
* } else if (SepPoly == true && SepLev == false) {
* title = string.Format("(var#{0},p={1})", iVar, pDG);
* } else if (SepPoly == true && SepLev == true) {
* title = string.Format("(var#{0},mg.lev.{1},p={2})", iVar, iLevel, pDG);
* } else {
* throw new ApplicationException();
* }
*/
int iColKv = titleS.IndexOf(title);
if (iColKv < 0)
{
titleS.Add(title);
iColKv = iCol;
iCol++;
}
ColumnIndex.Add(kv.Key, iColKv);
}
Titels = titleS.ToArray();
ConvTrendData = MultidimensionalArray.Create(data.First().Value.Count, titleS.Count);
foreach (var kv in data) // over all data columns
{
double[] ColumnSquared = kv.Value.Select(val => val.Pow2()).ToArray();
if (ConvTrendData.GetLength(0) != ColumnSquared.Length)
{
throw new ApplicationException();
}
int iColkv = ColumnIndex[kv.Key]; // output column index in which we sum up the column
ConvTrendData.ExtractSubArrayShallow(-1, iColkv).AccVector(1.0, ColumnSquared);
}
ConvTrendData.ApplyAll(x => Math.Sqrt(x));
}
protected override bool HeightDirectionIsSuitable(
LinearSayeSpace <Cube> arg,
LinearPSI <Cube> psi, NodeSet
x_center,
int heightDirection,
MultidimensionalArray agradient, int cell)
{
//throw new NotImplementedException();
//Determine bounds
//-----------------------------------------------------------------------------------------------------------------
NodeSet nodeOnPsi = psi.ProjectOnto(x_center);
MultidimensionalArray jacobian = grid.Jacobian.GetValue_Cell(nodeOnPsi, cell, 1);
jacobian = jacobian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 });
LevelSet levelSet = lsData.LevelSet as LevelSet;
MultidimensionalArray hessian = MultidimensionalArray.Create(1, 1, 3, 3);
levelSet.EvaluateHessian(cell, 1, nodeOnPsi, hessian);
hessian = hessian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 }).CloneAs();
//hessian = jacobian * hessian;
hessian.ApplyAll(x => Math.Abs(x));
MultidimensionalArray gradient = lsData.GetLevelSetGradients(nodeOnPsi, cell, 1);
gradient = gradient.ExtractSubArrayShallow(0, 0, -1).CloneAs();
//abs(Hessian) * 0,5 * diameters.^2 = delta ,( square each entry of diameters) ,
//this bounds the second error term from taylor series
//+ + + +
double[] arr = arg.Diameters.CloneAs();
psi.SetInactiveDimsToZero(arr);
MultidimensionalArray diameters = MultidimensionalArray.CreateWrapper(arr, 3, 1);
diameters = jacobian * diameters;
diameters.ApplyAll(x => 0.5 * x * x);
MultidimensionalArray delta = hessian * diameters;
delta = delta.ExtractSubArrayShallow(-1, 0);
//Check if suitable
//-----------------------------------------------------------------------------------------------------------------
//|gk| > δk
//Gradient should be able to turn arround
psi.SetInactiveDimsToZero(gradient.Storage);
if (Math.Abs(gradient[heightDirection]) > delta[heightDirection])
{
bool suitable = true;
// ||Grad + maxChange|| should be smaller than 20 *
// Sum_j( g_j + delta_j)^2 / (g_k - delta_k)^2 < 20
double sum = 0;
for (int j = 0; j < delta.Length; ++j)
{
sum += Math.Pow(Math.Abs(gradient[j]) + delta[j], 2);
}
sum /= Math.Pow(Math.Abs(gradient[heightDirection]) - delta[heightDirection], 2);
suitable &= sum < 20;
return(suitable);
}
return(false);
}
