/// <summary>
/// Given a set of Heaviside enriched nodes, find which of them must not be enriched, in order to avoid the global
/// stiffness matrix being singular.
/// </summary>
/// <param name="mesh"></param>
/// <param name="heavisideNodes">They will not be altered.</param>
/// <returns></returns>
public ISet <XNode> FindHeavisideNodesToRemove(ISingleCrack crack, IMesh2D <XNode, XContinuumElement2D> mesh,
ISet <XNode> heavisideNodes)
{
var processedElements = new Dictionary <XContinuumElement2D, Tuple <double, double> >();
var nodesToRemove = new HashSet <XNode>();
foreach (var node in heavisideNodes)
{
double nodePositiveArea = 0.0;
double nodeNegativeArea = 0.0;
foreach (var element in mesh.FindElementsWithNode(node))
{
bool alreadyProcessed = processedElements.TryGetValue(element, out Tuple <double, double> elementPosNegAreas);
if (!alreadyProcessed)
{
(double elementPosArea, double elementNegArea) = FindSignedAreasOfElement(crack, element);
elementPosNegAreas = new Tuple <double, double>(elementPosArea, elementNegArea);
processedElements[element] = elementPosNegAreas;
}
nodePositiveArea += elementPosNegAreas.Item1;
nodeNegativeArea += elementPosNegAreas.Item2;
}
if (crack.SignedDistanceOf(node) >= 0.0)
{
double negativeAreaRatio = nodeNegativeArea / (nodePositiveArea + nodeNegativeArea);
if (negativeAreaRatio < relativeAreaTolerance)
{
nodesToRemove.Add(node);
}
}
else
{
double positiveAreaRatio = nodePositiveArea / (nodePositiveArea + nodeNegativeArea);
if (positiveAreaRatio < relativeAreaTolerance)
{
nodesToRemove.Add(node);
}
}
}
return(nodesToRemove);
}
private HashSet <TElement> FindElementsWithCommonEdges(TElement element)
{
//TODO: At least 2 common nodes works for 1st order elements, but what about 2nd order ones?
//TODO: Perhaps I should implement a method to get the Edge of an element and work with that one.
// Find all elements with at least one common node. Also store the common nodes.
var allNeighbors = new Dictionary <TElement, HashSet <INode> >();
foreach (TNode node in element.Nodes)
{
foreach (TElement neighbor in mesh.FindElementsWithNode(node))
{
bool neighborIsKnown = allNeighbors.TryGetValue(neighbor, out HashSet <INode> commonNodes);
if (!neighborIsKnown)
{
commonNodes = new HashSet <INode>();
allNeighbors.Add(neighbor, commonNodes);
}
commonNodes.Add(node);
}
}
allNeighbors.Remove(element); // The same element may be added by the above procedure.
// Only keep the elements that have 2 or more common nodes.
var elementsWithCommonEdge = new HashSet <TElement>();
foreach (var neighborNodesPair in allNeighbors)
{
if (neighborNodesPair.Value.Count > 1)
{
elementsWithCommonEdge.Add(neighborNodesPair.Key);
}
}
return(elementsWithCommonEdge);
}