/// <summary>
/// Determines the total curvature which is twice the mean curvature
/// Please pay attention to the sign of this expression!
/// </summary>
/// <param name="Output">The total curvature</param>
/// <param name="optionalSubGrid">
/// Subgrid which can be defined, for example for carrying out
/// computations on a narrow band
/// </param>
/// <param name="bndMode">
/// Definition of the behavior at subgrid boundaries
/// </param>
public void ComputeTotalCurvatureByFlux(SinglePhaseField Output,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
if (this.m_Basis.Degree <= 1)
{
throw new ArgumentException("For correct computation of these level set quantities, the level set has to be at least of degree 2!");
}
Basis basisForNormalVec = new Basis(this.GridDat, this.m_Basis.Degree - 1);
Basis basisForCurvature = new Basis(this.GridDat, this.m_Basis.Degree - 2);
Func <Basis, string, SinglePhaseField> fac = (Basis b, string id) => new SinglePhaseField(b, id);
VectorField <SinglePhaseField> normalVector = new VectorField <SinglePhaseField>(this.GridDat.SpatialDimension, basisForNormalVec, fac);
ComputeNormalByFlux(normalVector, optionalSubGrid, bndMode);
VectorField <SinglePhaseField> secondDerivatives = new VectorField <SinglePhaseField>(this.GridDat.SpatialDimension, basisForCurvature, fac);
Output.Clear();
for (int i = 0; i < normalVector.Dim; i++)
{
secondDerivatives[i].DerivativeByFlux(1.0, normalVector[i], i, optionalSubGrid, bndMode);
Output.Acc(-1.0, secondDerivatives[i], optionalSubGrid.VolumeMask);
}
}
/// <summary>
/// see <see cref="DGField.LaplacianByFlux(double,DGField,DGField,SubGrid,SpatialOperator.SubGridBoundaryModes,SpatialOperator.SubGridBoundaryModes)"/>;
/// </summary>
override public void LaplacianByFlux(double alpha, DGField f, DGField tmp,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode_1stDeriv = SpatialOperator.SubGridBoundaryModes.OpenBoundary,
SpatialOperator.SubGridBoundaryModes bndMode_2ndDeriv = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
if (tmp == null)
{
// the base implementation will create the temporary field by cloning, which is a bad idea for
// the species-shadow-field
tmp = new SinglePhaseField(this.Basis, "tmp");
}
base.LaplacianByFlux(alpha, f, tmp, optionalSubGrid, bndMode_1stDeriv, bndMode_2ndDeriv);
}
/// <summary>
/// accumulates the curl of 2D DG vector field <paramref name="vec"/>
/// times <paramref name="alpha"/>
/// to this vector field, i.e. <br/>
/// this = this + <paramref name="alpha"/>* Curl(<paramref name="vec"/>)
/// </summary>
/// <param name="alpha"></param>
/// <param name="vec"></param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)
/// <br/>
/// if null, the computation is carried out in the whole domain.
/// </param>
/// <remarks>
/// This method is based on <see cref="DGField.DerivativeByFlux"/>, i.e.
/// it calculates derivatives by central-difference fluxes;
/// </remarks>
/// <seealso cref="VectorField{T}.Curl3DByFlux"/>
/// <param name="bndMode"></param>
public void Curl2DByFlux <T>(double alpha, VectorField <T> vec,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
where T : DGField
{
//diff(v(x, y), x)-(diff(u(x, y), y))
using (new FuncTrace()) {
if (vec.Dim != 2)
{
throw new ArgumentException("vector field must be 2-dim.", "vec");
}
this.DerivativeByFlux(alpha, vec[1], 0, optionalSubGrid, bndMode);
this.DerivativeByFlux(-alpha, vec[0], 1, optionalSubGrid, bndMode);
}
}
/// <summary>
/// accumulates the divergence of vector field <paramref name="vec"/>
/// times <paramref name="alpha"/>
/// to this field.
/// </summary>
/// <remarks>
/// This method is based on <see cref="DerivativeByFlux"/>;
/// </remarks>
public void DivergenceByFlux <T>(double alpha, VectorField <T> vec,
SubGrid optionalSubGrid = null, SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary) where T : DGField
{
using (new FuncTrace()) {
if (vec.Dim != GridDat.SpatialDimension)
{
throw new ArgumentException("wrong number of components in vector field.", "vec");
}
int D = GridDat.SpatialDimension;
for (int d = 0; d < D; d++)
{
this.DerivativeByFlux(alpha, vec[d], d, optionalSubGrid, bndMode);
}
}
}
/// <summary>
/// Accumulates the derivative of <paramref name="f"/> with respect to
/// x_i to the i-th component of this vector field by making use of
/// <see cref="DGField.DerivativeByFlux"/>
/// </summary>
/// <param name="alpha"></param>
/// <param name="f"></param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="Grid.GridData.BoundaryCells"/>.)
/// <br/>
/// if null, the computation is carried out in the whole domain.
/// </param>
/// <param name="bndMode">
/// </param>
public void GradientByFlux(
double alpha,
DGField f,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
int D = f.Basis.GridDat.SpatialDimension;
if (this.Dim != D)
{
throw new NotSupportedException("this field has not the right spatial dimension");
}
for (int d = 0; d < D; d++)
{
this.m_Components[d].DerivativeByFlux(alpha, f, d, optionalSubGrid, bndMode);
}
}
/// <summary>
/// accumulates the Laplacian of field <paramref name="f"/> times
/// <paramref name="alpha"/> to this field.
/// </summary>
/// <param name="alpha"></param>
/// <param name="f"></param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)
/// <br/>
/// if null, the computation is carried out in the whole domain.
/// </param>
/// <param name="tmp">
/// temporary storage needed for the 1st derivatives of
/// <paramref name="f"/>; If null, a clone of <paramref name="f"/>
/// is taken.
/// </param>
/// <param name="bndMode_1stDeriv"></param>
/// <param name="bndMode_2ndDeriv"></param>
/// <remarks>
/// This method is based on <see cref="DGField.DerivativeByFlux"/>,
/// i.e. it calculates derivatives by central-difference fluxes;<br/>
/// Note that of the Laplacian requires the allocation of a temporary DG field.
/// </remarks>
virtual public void LaplacianByFlux(double alpha, DGField f, DGField tmp = null,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode_1stDeriv = SpatialOperator.SubGridBoundaryModes.OpenBoundary,
SpatialOperator.SubGridBoundaryModes bndMode_2ndDeriv = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
using (new FuncTrace()) {
if (tmp == null)
{
tmp = (DGField)f.Clone();
}
int D = GridDat.SpatialDimension;
for (int d = 0; d < D; d++)
{
tmp.Clear();
tmp.DerivativeByFlux(1.0, f, d, optionalSubGrid, bndMode_1stDeriv);
this.DerivativeByFlux(alpha, tmp, d, optionalSubGrid, bndMode_2ndDeriv);
}
}
}
/// <summary>
/// accumulates the curl of 3D DG vector field <paramref name="vec"/>
/// times <paramref name="alpha"/>
/// to this vector field, i.e. <br/>
/// this = this + <paramref name="alpha"/>* Curl(<paramref name="vec"/>)
/// </summary>
/// <param name="alpha"></param>
/// <param name="vec"></param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="Grid.GridData.BoundaryCells"/>.)
/// <br/> if null, the computation is carried out in the whole domain.
/// </param>
/// <param name="bndMode"></param>
/// <remarks>
/// This method is based on
/// <see cref="DGField.DerivativeByFlux(double,DGField,int,SubGrid,SpatialOperator.SubGridBoundaryModes)"/>,
/// i.e. it calculates derivatives by central-difference fluxes;
/// </remarks>
/* <seealso cref="DGField.Curl2DByFlux{T}"/> */
public void Curl3DByFlux(double alpha, VectorField <T> vec,
SubGrid optionalSubGrid = null, SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
if (vec.Dim != 3)
{
throw new ArgumentException("this method works only for 3-dimensional vector fields.", "vec");
}
if (this.Dim != 3)
{
throw new ApplicationException("this vector field must be 3-dimensional.");
}
this.m_Components[0].DerivativeByFlux(alpha, vec.m_Components[2], 1, optionalSubGrid, bndMode);
this.m_Components[0].DerivativeByFlux(-alpha, vec.m_Components[1], 2, optionalSubGrid, bndMode);
this.m_Components[1].DerivativeByFlux(alpha, vec.m_Components[0], 2, optionalSubGrid, bndMode);
this.m_Components[1].DerivativeByFlux(-alpha, vec.m_Components[2], 0, optionalSubGrid, bndMode);
this.m_Components[2].DerivativeByFlux(alpha, vec.m_Components[1], 0, optionalSubGrid, bndMode);
this.m_Components[2].DerivativeByFlux(-alpha, vec.m_Components[0], 1, optionalSubGrid, bndMode);
}
/// <summary>
/// Vector of the d partial derivatives of the i-th component of the
/// normal vector
/// </summary>
/// <param name="Output">Vector of the partial derivatives</param>
/// <param name="componentOfNormalVec">
/// specifies the component i of the normal vector
/// </param>
/// <param name="optionalSubGrid"></param>
/// <param name="bndMode"></param>
public void ComputeDerivativesOfTheNormalByFlux(
VectorField <SinglePhaseField> Output,
int componentOfNormalVec,
SubGrid optionalSubGrid = null,
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
if (this.m_Basis.Degree <= 1)
{
throw new ArgumentException("For correct computation of these level set quantities, the level set has to be at least of degree 2!");
}
Basis basisForNormalVec = new Basis(this.GridDat, this.m_Basis.Degree - 1);
Func <Basis, string, SinglePhaseField> fac = (Basis b, string id) => new SinglePhaseField(b, id);
VectorField <SinglePhaseField> normalVector = new VectorField <SinglePhaseField>(this.GridDat.SpatialDimension, basisForNormalVec, fac);
ComputeNormalByFlux(normalVector, optionalSubGrid, bndMode);
for (int i = 0; i < Output.Dim; i++)
{
Output[i].DerivativeByFlux(1.0, normalVector[componentOfNormalVec], i, optionalSubGrid, bndMode);
}
}
/// <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)
);
}
}
/// <summary>
/// Assigns the normalized gradient of the level set to the Output
/// vector
/// </summary>
/// <param name="Output">Normal vector</param>
/// <param name="optionalSubGrid">
/// Restriction of the computations to a an optional subgrid
/// </param>
/// <param name="bndMode"></param>
public void ComputeNormalByFlux(VectorField <SinglePhaseField> Output, SubGrid optionalSubGrid = null, SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
if (this.m_Basis.Degree < 1)
{
throw new ArgumentException("For correct computation of these level set quantities, the level set has to be at least of degree 1!");
}
SinglePhaseField absval = new SinglePhaseField(Output[0].Basis);
//Output.Clear();
for (int i = 0; i < Output.Dim; i++)
{
Output[i].DerivativeByFlux(1.0, this, i, optionalSubGrid, bndMode);
}
absval.ProjectAbs(1.0, Output);
for (int i = 0; i < Output.Dim; i++)
{
Output[i].ProjectQuotient(1.0, Output[i], absval, null, false);
}
}
/// <summary>
///
/// </summary>
/// <param name="spatialOp"></param>
/// <param name="Fieldsmap"></param>
/// <param name="Parameters">
/// optional parameter fields, can be null if
/// <paramref name="spatialOp"/> contains no parameters; must match
/// the parameter field list of <paramref name="spatialOp"/>, see
/// <see cref="BoSSS.Foundation.SpatialOperator.ParameterVar"/>
/// </param>
/// <param name="sgrdBnd">
/// Options for the treatment of edges at the boundary of a SubGrid,
/// <see cref="SpatialOperator.SubGridBoundaryModes"/></param>
/// <param name="timeStepConstraints">
/// optional list of time step constraints <see cref="TimeStepConstraint"/>
/// </param>
/// <param name="sgrd">
/// optional restriction to computational domain
/// </param>
public ExplicitEuler(SpatialOperator spatialOp, CoordinateMapping Fieldsmap, CoordinateMapping Parameters, SpatialOperator.SubGridBoundaryModes sgrdBnd, IList <TimeStepConstraint> timeStepConstraints = null, SubGrid sgrd = null)
{
using (new ilPSP.Tracing.FuncTrace()) {
// verify input
// ============
if (!spatialOp.ContainsNonlinear && !(spatialOp.ContainsLinear()))
{
throw new ArgumentException("spatial differential operator seems to contain no components.", "spatialOp");
}
if (spatialOp.DomainVar.Count != spatialOp.CodomainVar.Count)
{
throw new ArgumentException("spatial differential operator must have the same number of domain and codomain variables.", "spatialOp");
}
if (Fieldsmap.Fields.Count != spatialOp.CodomainVar.Count)
{
throw new ArgumentException("the number of fields in the coordinate mapping must be equal to the number of domain/codomain variables of the spatial differential operator", "fields");
}
if (Parameters == null)
{
if (spatialOp.ParameterVar.Count != 0)
{
throw new ArgumentException("the number of fields in the parameter mapping must be equal to the number of parameter variables of the spatial differential operator", "Parameters");
}
}
else
{
if (Parameters.Fields.Count != spatialOp.ParameterVar.Count)
{
throw new ArgumentException("the number of fields in the parameter mapping must be equal to the number of parameter variables of the spatial differential operator", "Parameters");
}
}
Mapping = Fieldsmap;
DGCoordinates = new CoordinateVector(Mapping);
ParameterMapping = Parameters;
IList <DGField> ParameterFields =
(ParameterMapping == null) ? (new DGField[0]) : ParameterMapping.Fields;
this.TimeStepConstraints = timeStepConstraints;
SubGrid = sgrd ?? new SubGrid(CellMask.GetFullMask(Fieldsmap.First().GridDat));
// generate Evaluator
// ==================
CellMask cm = SubGrid.VolumeMask;
EdgeMask em = SubGrid.AllEdgesMask;
Operator = spatialOp;
m_Evaluator = new Lazy <SpatialOperator.Evaluator>(() => spatialOp.GetEvaluatorEx(
Fieldsmap, ParameterFields, Fieldsmap,
new EdgeQuadratureScheme(true, em),
new CellQuadratureScheme(true, cm),
SubGrid,
sgrdBnd));
}
}
/// <summary>
///
/// </summary>
/// <param name="spatialOp"></param>
/// <param name="Fieldsmap"></param>
/// <param name="Parameters">
/// optional parameter fields, can be null if
/// <paramref name="spatialOp"/> contains no parameters; must match
/// the parameter field list of <paramref name="spatialOp"/>, see
/// <see cref="BoSSS.Foundation.SpatialOperator.ParameterVar"/>
/// </param>
/// <param name="sgrdBnd">
/// Options for the treatment of edges at the boundary of a SubGrid,
/// <see cref="SpatialOperator.SubGridBoundaryModes"/></param>
/// <param name="timeStepConstraints">
/// optional list of time step constraints <see cref="TimeStepConstraint"/>
/// </param>
/// <param name="sgrd">
/// optional restriction to computational domain
/// </param>
public ExplicitEuler(SpatialOperator spatialOp, CoordinateMapping Fieldsmap, CoordinateMapping Parameters, SpatialOperator.SubGridBoundaryModes sgrdBnd, IList <TimeStepConstraint> timeStepConstraints = null, SubGrid sgrd = null)
{
using (new ilPSP.Tracing.FuncTrace()) {
// verify input
// ============
TimeStepperCommon.VerifyInput(spatialOp, Fieldsmap, Parameters);
Mapping = Fieldsmap;
CurrentState = new CoordinateVector(Mapping);
ParameterMapping = Parameters;
IList <DGField> ParameterFields =
(ParameterMapping == null) ? (new DGField[0]) : ParameterMapping.Fields;
this.TimeStepConstraints = timeStepConstraints;
SubGrid = sgrd ?? new SubGrid(CellMask.GetFullMask(Fieldsmap.First().GridDat));
// generate Evaluator
// ==================
CellMask cm = SubGrid.VolumeMask;
EdgeMask em = SubGrid.AllEdgesMask;
Operator = spatialOp;
m_Evaluator = new Lazy <SpatialOperator.Evaluator>(() => spatialOp.GetEvaluatorEx(
Fieldsmap, ParameterFields, Fieldsmap,
new EdgeQuadratureScheme(true, em),
new CellQuadratureScheme(true, cm),
SubGrid,
sgrdBnd));
}
}
/// <summary>
/// Evaluates this operator for given DG fields;
/// </summary>
/// <param name="DomainMapping">
/// the domain variables, or "input data" for the operator; the number
/// of elements must be equal to the number of elements in the
/// <see cref="DomainVar"/>-list;
/// </param>
/// <param name="Params">
/// List of parameter fields; May be null
/// </param>
/// <param name="CodomainMapping">
/// the co-domain variables, or "output" for the evaluation of the
/// operator; the number of elements must be equal to the number of
/// elements in the <see cref="CodomainVar"/>-list;
/// </param>
/// <param name="alpha">
/// scaling of the operator
/// </param>
/// <param name="beta">
/// scaling of the accumulator (<paramref name="CodomainMapping"/>);
/// </param>
/// <param name="sgrd">
/// subgrid, for restricted evaluation; null indicates evaluation on
/// the full grid.
/// </param>
/// <param name="bndMode">
/// Treatment of subgrid boundaries, if <paramref name="sgrd"/> is not
/// null. See <see cref="Evaluator"/>
/// </param>
/// <param name="qInsEdge">
/// Optional definition of the edge quadrature scheme. Since this
/// already implies a domain of integration, must be null if
/// <paramref name="sgrd"/> is not null.
/// </param>
/// <param name="qInsVol">
/// Optional definition of the volume quadrature scheme. Since this
/// already implies a domain of integration, must be null if
/// <paramref name="sgrd"/> is not null.
/// </param>
/// <remarks>
/// If some of the input data, <paramref name="DomainMapping"/>, is
/// contained in the output data, <paramref name="CodomainMapping"/>,
/// these DG fields will be cloned to ensure correct operation of the
/// operator evaluation.<br/>
/// It is not a good choice to use this function if this operator
/// should be evaluated multiple times and contains linear components
/// (i.e. <see cref="ContainsLinear"/> returns true); If the latter is
/// the case, the matrix which represents the linear components of the
/// operator must be computed first, which is computational- and
/// memory-intensive; After execution of this method, the matrix will
/// be lost; If multiple evaluation is desired, the
/// <see cref="Evaluator"/>-class should be used, in which the matrix
/// of the operator will persist; However, if no linear components are
/// present, the performance of this function should be almost
/// comparable to the use of the <see cref="Evaluator"/>-class;
/// </remarks>
static public void Evaluate(
this SpatialOperator op,
double alpha, double beta,
CoordinateMapping DomainMapping, IList <DGField> Params, CoordinateMapping CodomainMapping,
SubGrid sgrd = null,
EdgeQuadratureScheme qInsEdge = null,
CellQuadratureScheme qInsVol = null,
SpatialOperator.SubGridBoundaryModes bndMode = SubGridBoundaryModes.OpenBoundary,
double time = double.NaN) //
{
using (new FuncTrace()) {
if (sgrd != null && (qInsEdge != null || qInsVol != null))
{
throw new ArgumentException("Specification of Subgrid and quadrature schemes is exclusive: not allowed to specify both at the same time.", "sgrd");
}
#if DEBUG
op.Verify(); //this has already been done during this.Commit()
#endif
IList <DGField> _DomainFields = DomainMapping.Fields;
IList <DGField> _CodomainFields = CodomainMapping.Fields;
DGField[] _DomainFieldsRevisited = new DGField[_DomainFields.Count];
bool a = false;
for (int i = 0; i < _DomainFields.Count; i++)
{
DGField f = _DomainFields[i];
if (_CodomainFields.Contains(f))
{
// some of the domain variables (input data)
// is also a member of the codomain variables (output);
// the data need to be cloned to provide correct results
a = true;
_DomainFieldsRevisited[i] = (DGField)f.Clone();
}
else
{
_DomainFieldsRevisited[i] = f;
}
}
CoordinateMapping domainMappingRevisited;
if (a)
{
domainMappingRevisited = new CoordinateMapping(_DomainFieldsRevisited);
}
else
{
domainMappingRevisited = DomainMapping;
}
if (sgrd != null)
{
CellMask cm = (sgrd == null) ? null : sgrd.VolumeMask;
EdgeMask em = (sgrd == null) ? null : sgrd.AllEdgesMask;
qInsEdge = new EdgeQuadratureScheme(true, em);
qInsVol = new CellQuadratureScheme(true, cm);
}
var ev = op.GetEvaluatorEx(
domainMappingRevisited, Params, CodomainMapping,
qInsEdge,
qInsVol);
if (sgrd != null)
{
ev.ActivateSubgridBoundary(sgrd.VolumeMask, bndMode);
}
CoordinateVector outp = new CoordinateVector(CodomainMapping);
ev.time = time;
ev.Evaluate <CoordinateVector>(alpha, beta, outp);
}
}
/// <summary>
/// accumulates the derivative of DG field <paramref name="f"/>
/// (along the <paramref name="d"/>-th axis) times <paramref name="alpha"/>
/// to this field, i.e. <br/>
/// this = this + <paramref name="alpha"/>* \f$ \frac{\partial}{\partial x_d} \f$ <paramref name="f"/>;
/// </summary>
/// <param name="f"></param>
/// <param name="d">
/// 0 for the x-derivative, 1 for the y-derivative, 2 for the
/// z-derivative
/// </param>
/// <param name="alpha">
/// scaling of <paramref name="f"/>;
/// </param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)
/// <br/>
/// if null, the computation is carried out in the whole domain.
/// </param>
/// <param name="bndMode">
/// if a sub-grid is provided, this determines how the sub-grid
/// boundary should be treated.
/// </param>
/// <remarks>
/// The derivative is calculated using Riemann flux functions
/// (central difference);<br/>
/// In comparison to
/// <see cref="Derivative(double, DGField, int, CellMask)"/>, this method
/// should be slower, but produce more sane results, especially for
/// fields of low polynomial degree (0 or 1);
/// </remarks>
virtual public void DerivativeByFlux(double alpha, DGField f, int d, SubGrid optionalSubGrid = null, SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary)
{
int D = this.Basis.GridDat.SpatialDimension;
if (d < 0 || d >= D)
{
throw new ArgumentException("spatial dimension out of range.", "d");
}
MPICollectiveWatchDog.Watch(csMPI.Raw._COMM.WORLD);
SpatialOperator d_dx = new SpatialOperator(1, 1, QuadOrderFunc.Linear(), "in", "out");
var flux = CreateDerivativeFlux(d, f.Identification);
d_dx.EquationComponents["out"].Add(flux);
d_dx.Commit();
EdgeMask emEdge = (optionalSubGrid != null) ? optionalSubGrid.AllEdgesMask : null;
CellMask emVol = (optionalSubGrid != null) ? optionalSubGrid.VolumeMask : null;
var ev = d_dx.GetEvaluatorEx(
new CoordinateMapping(f), null, this.Mapping,
edgeQrCtx: new Quadrature.EdgeQuadratureScheme(true, emEdge),
volQrCtx: new Quadrature.CellQuadratureScheme(true, emVol));
if (optionalSubGrid != null)
{
ev.ActivateSubgridBoundary(optionalSubGrid.VolumeMask, bndMode);
}
ev.Evaluate <CoordinateVector>(alpha, 1.0, this.CoordinateVector);
}
