void PrescribedGradientBCWeak :: assembleTangentGPContributionNew(FloatMatrix &oTangent, TracSegArray &iEl, GaussPoint &iGP, const double &iScaleFactor, const FloatArray &iBndCoord)
{
int dim = domain->giveNumberOfSpatialDimensions();
double detJ = 0.5 * iEl.giveLength();
//////////////////////////////////
// Compute traction N-matrix
// For now, assume piecewise constant approx
FloatArray Ntrac = FloatArray { 1.0 };
FloatMatrix NtracMat;
NtracMat.beNMatrixOf(Ntrac, dim);
//////////////////////////////////
// Compute displacement N-matrix
// Identify the displacement element
// we are currently standing in
// and compute local coordinates on
// the displacement element
SpatialLocalizer *localizer = domain->giveSpatialLocalizer();
FloatArray dispElLocCoord, closestPoint;
Element *dispEl = localizer->giveElementClosestToPoint(dispElLocCoord, closestPoint, iBndCoord );
// Compute basis functions
XfemElementInterface *xfemElInt = dynamic_cast< XfemElementInterface * >( dispEl );
FloatMatrix NdispMat;
if ( xfemElInt != NULL && domain->hasXfemManager() ) {
// If the element is an XFEM element, we use the XfemElementInterface to compute the N-matrix
// of the enriched element.
xfemElInt->XfemElementInterface_createEnrNmatrixAt(NdispMat, dispElLocCoord, * dispEl, false);
} else {
// Otherwise, use the usual N-matrix.
const int numNodes = dispEl->giveNumberOfDofManagers();
FloatArray N(numNodes);
const int dim = dispEl->giveSpatialDimension();
NdispMat.resize(dim, dim * numNodes);
NdispMat.zero();
dispEl->giveInterpolation()->evalN( N, dispElLocCoord, FEIElementGeometryWrapper(dispEl) );
NdispMat.beNMatrixOf(N, dim);
}
FloatMatrix contrib;
contrib.beTProductOf(NtracMat, NdispMat);
contrib.times( iScaleFactor * detJ * iGP.giveWeight() );
oTangent = contrib;
}
void PrescribedGradientBCNeumann :: integrateTangent(FloatMatrix &oTangent, Element *e, int iBndIndex)
{
FloatArray normal, n;
FloatMatrix nMatrix, E_n;
FloatMatrix contrib;
Domain *domain = e->giveDomain();
XfemElementInterface *xfemElInt = dynamic_cast< XfemElementInterface * >( e );
FEInterpolation *interp = e->giveInterpolation(); // Geometry interpolation
int nsd = e->giveDomain()->giveNumberOfSpatialDimensions();
// Interpolation order
int order = interp->giveInterpolationOrder();
IntegrationRule *ir = NULL;
IntArray edgeNodes;
FEInterpolation2d *interp2d = dynamic_cast< FEInterpolation2d * >( interp );
if ( interp2d == NULL ) {
OOFEM_ERROR("failed to cast to FEInterpolation2d.")
}
interp2d->computeLocalEdgeMapping(edgeNodes, iBndIndex);
const FloatArray &xS = * ( e->giveDofManager( edgeNodes.at(1) )->giveCoordinates() );
const FloatArray &xE = * ( e->giveDofManager( edgeNodes.at( edgeNodes.giveSize() ) )->giveCoordinates() );
if ( xfemElInt != NULL && domain->hasXfemManager() ) {
std :: vector< Line >segments;
std :: vector< FloatArray >intersecPoints;
xfemElInt->partitionEdgeSegment(iBndIndex, segments, intersecPoints);
MaterialMode matMode = e->giveMaterialMode();
ir = new DiscontinuousSegmentIntegrationRule(1, e, segments, xS, xE);
int numPointsPerSeg = 1;
ir->SetUpPointsOnLine(numPointsPerSeg, matMode);
} else {
ir = interp->giveBoundaryIntegrationRule(order, iBndIndex);
}
oTangent.clear();
for ( GaussPoint *gp: *ir ) {
FloatArray &lcoords = * gp->giveNaturalCoordinates();
FEIElementGeometryWrapper cellgeo(e);
// Evaluate the normal;
double detJ = interp->boundaryEvalNormal(normal, iBndIndex, lcoords, cellgeo);
interp->boundaryEvalN(n, iBndIndex, lcoords, cellgeo);
// If cracks cross the edge, special treatment is necessary.
// Exploit the XfemElementInterface to minimize duplication of code.
if ( xfemElInt != NULL && domain->hasXfemManager() ) {
// Compute global coordinates of Gauss point
FloatArray globalCoord;
interp->boundaryLocal2Global(globalCoord, iBndIndex, lcoords, cellgeo);
// Compute local coordinates on the element
FloatArray locCoord;
e->computeLocalCoordinates(locCoord, globalCoord);
xfemElInt->XfemElementInterface_createEnrNmatrixAt(nMatrix, locCoord, * e, false);
} else {
// Evaluate the velocity/displacement coefficients
nMatrix.beNMatrixOf(n, nsd);
}
if ( nsd == 3 ) {
OOFEM_ERROR("not implemented for nsd == 3.")
} else if ( nsd == 2 ) {
E_n.resize(4, 2);
E_n.at(1, 1) = normal.at(1);
E_n.at(1, 2) = 0.0;
E_n.at(2, 1) = 0.0;
E_n.at(2, 2) = normal.at(2);
E_n.at(3, 1) = normal.at(2);
E_n.at(3, 2) = 0.0;
E_n.at(4, 1) = 0.0;
E_n.at(4, 2) = normal.at(1);
} else {
E_n.clear();
}
contrib.beProductOf(E_n, nMatrix);
oTangent.add(detJ * gp->giveWeight(), contrib);
}
delete ir;
}