public static double CalculateError(IFiniteElementSpace feSpace,
Func <double, double, double> exactSolution, FiniteElementVectorField solution)
{
double squareError = 0;
foreach (var element in feSpace.FiniteElements)
{
Func <Vector2, double> error = v =>
{
double u0 = exactSolution(v.x, v.y),
uh0 = 0;
foreach (var node in element.Nodes)
{
uh0 += node.Phi(v) * solution.GetValueAt(node.Vertex, 0);
}
return((u0 - uh0) * (u0 - uh0));
};
squareError += quadrature.Integrate(error, element.Triangle);
}
return(Math.Sqrt(squareError));
}
public FiniteElementScalarField(IFiniteElementSpace finiteElementSpace, IEnumerable <double> values)
{
this.finiteElementSpace = finiteElementSpace;
int n = finiteElementSpace.Vertices.Count;
valueByVertex = new Dictionary <Vertex, double>(n);
int valueCount = 0;
var valueEnumerator = values.GetEnumerator();
foreach (var vertex in finiteElementSpace.Vertices)
{
valueEnumerator.MoveNext();
var value = valueEnumerator.Current;
valueByVertex.Add(vertex, value);
valueCount++;
}
if (valueCount != n)
{
throw new ArgumentException($"The number of values ({valueCount}) does not match the number of vertices ({n}).");
}
}
public Problem(IFiniteElementSpace finiteElementSpace,
Dictionary <int, IVectorField> boundaryConditions,
BilinearForm bilinearForm, IVectorField rightHandSide,
ISolver solver = null, IQuadrature quadrature = null)
{
this.finiteElementSpace = finiteElementSpace;
this.boundaryConditions = boundaryConditions;
this.bilinearForm = bilinearForm;
this.rightHandSide = rightHandSide;
var dim = rightHandSide.Dimension;
var mismatch = boundaryConditions.Values
.Any(condition => condition.Dimension != dim);
if (mismatch)
{
throw new ArgumentException("Dimension mismatched.");
}
// TODO: Validate bilinear form.
this.solver = solver ?? new ConjugateGradient(1e-6);
this.quadrature = quadrature ?? new GaussianQuadrature();
}