/*----------------------------------------------------------------------*
| mwgee 08/05|
| 2D case: |
| this method evaluates the function |
| F(eta) = ( Ni * xis - xm ) dot g(xi) |
| with Ni shape functions of slave segment |
| xm nodal coords of master node |
| xs nodal coords of slave nodes on segment |
| njs nodal outward normal of nodes xs (slave side) |
*----------------------------------------------------------------------*/
double MOERTEL::Projector::evaluate_F_2D_SegmentOrthogonal(MOERTEL::Node& node,
MOERTEL::Segment& seg,
double eta,
double &gap)
{
// check the type of function on the segment
// Here, we need 1D functions set as function id 0
MOERTEL::Function::FunctionType type = seg.FunctionType(0);
if (type != MOERTEL::Function::func_Linear1D)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_F_2D_SegmentOrthogonal:\n"
<< "***ERR*** function is of wrong type\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// evaluate the first function set on segment at eta
int nsnode = seg.Nnode();
double val[100];
seg.EvaluateFunction(0,&eta,val,nsnode,NULL);
// get nodal coords and normals of slave nodes and interpolate them
double Nx[2];
Nx[0] = Nx[1] = 0.0;
MOERTEL::Node** snodes = seg.Nodes();
if (!snodes)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_F_2D_SegmentOrthogonal:\n"
<< "***ERR*** segment " << seg.Id() << " ptr to it's nodes is zero\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
for (int i=0; i<nsnode; ++i)
{
const double* X = snodes[i]->X();
Nx[0] += val[i]*X[0];
Nx[1] += val[i]*X[1];
}
// subtract xm from interpolated coords Nx
const double* X = node.X();
Nx[0] -= X[0];
Nx[1] -= X[1];
// evaluate the metric of the segment in point xi
double g[2];
seg.Metric(&eta,g,NULL);
// calculate F
double F = Nx[0]*g[0] + Nx[1]*g[1];
gap = (Nx[0] * g[0] + Nx[1] * g[1]);
// gap = ((Nx[0] - X[0]) * g[0] + (Nx[1] - X[1]) * g[1])
// / sqrt(g[0] * g[0] + g[1] * g[1]); // ||gap|| cos theta
return F;
}
/*----------------------------------------------------------------------*
| mwgee 08/05|
| 2D case: |
| this method evaluates the function |
| gradF(eta) = |
| ( Ni,eta * xis ) * ( Ni,eta * xis ) |
| with Ni,eta derivative of shape functions of segment |
| Ni,Nj shape functions of segment |
| xis nodal coords of segment's nodes i (slave side) |
*----------------------------------------------------------------------*/
double MOERTEL::Projector::evaluate_gradF_2D_SegmentOrthogonal_to_g(
MOERTEL::Node& node,
MOERTEL::Segment& seg,
double eta,
double* g)
{
// check the type of function on the segment
// Here, we need 1D functions set as function id 0
MOERTEL::Function::FunctionType type = seg.FunctionType(0);
if (type != MOERTEL::Function::func_Linear1D)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_gradF_2D_SegmentOrthogonal_to_g:\n"
<< "***ERR*** function is of wrong type\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// evaluate function and derivatives of the first function set on segment at eta
int nmnode = seg.Nnode();
double deriv[200];
seg.EvaluateFunction(0,&eta,NULL,nmnode,deriv);
// intermediate data:
// Nxeta = Ni,eta * xi
// get nodal coords and normals of nodes and interpolate them
double Nxeta[2]; Nxeta[0] = Nxeta[1] = 0.0;
MOERTEL::Node** mnodes = seg.Nodes();
if (!mnodes)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_gradF_2D_SegmentOrthogonal_to_g:\n"
<< "***ERR*** segment " << seg.Id() << " ptr to it's nodes is zero\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
for (int i=0; i<nmnode; ++i)
{
const double* X = mnodes[i]->X();
Nxeta[0] += deriv[i]*X[0];
Nxeta[1] += deriv[i]*X[1];
}
// calculate gradF
double gradF = Nxeta[0]*g[0] + Nxeta[1]*g[1];
return gradF;
}
/*----------------------------------------------------------------------*
| mwgee 08/05|
*----------------------------------------------------------------------*/
bool MOERTEL::Projector::ProjectNodetoSegment_SegmentOrthogonal(MOERTEL::Node& node,
MOERTEL::Segment& seg,
double xi[],
double &gap)
{
#if 0
std::cout << "----- Projector: Node " << node.Id() << " Segment " << seg.Id() << std::endl;
#endif
if (IsTwoDimensional())
{
// we do a newton iteration for the projection coordinates xi
// set starting value to the middle of the segment
double eta = 0.0;
int i = 0;
double F=0.0,dF=0.0,deta=0.0;
for (i=0; i<10; ++i)
{
F = evaluate_F_2D_SegmentOrthogonal(node,seg,eta,gap);
if (abs(F) < 1.0e-10) break;
dF = evaluate_gradF_2D_SegmentOrthogonal(node,seg,eta);
deta = (-F)/dF;
eta += deta;
}
if (abs(F)>1.0e-10)
{
if (OutLevel()>3)
std::cout << "MOERTEL: ***WRN*** MOERTEL::Projector::ProjectNodetoSegment_SegmentOrthogonal:\n"
<< "MOERTEL: ***WRN*** Newton iteration failed to converge\n"
<< "MOERTEL: ***WRN*** #iterations = " << i << std::endl
<< "MOERTEL: ***WRN*** F(eta) = " << F << " gradF(eta) = " << dF << " eta = " << eta << " delta(eta) = " << deta << "\n"
<< "MOERTEL: ***WRN*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
}
#if 0
std::cout << "#iterations = " << i << " F = " << F << " eta = " << eta << std::endl;
#endif
xi[0] = eta;
return true;
}
else
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::ProjectNodetoSegment_SegmentOrthogonal:\n"
<< "***ERR*** 3D projection not yet impl.\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
return true;
}
/*----------------------------------------------------------------------*
| mwgee 08/05|
*----------------------------------------------------------------------*/
bool MOERTEL::Projector::ProjectNodetoSegment_Orthogonal_to_Slave(
MOERTEL::Node& snode,
MOERTEL::Segment& seg,
double xi[],
double &gap,
MOERTEL::Segment& sseg)
{
#if 0
std::cout << "----- Projector: Node " << snode.Id() << " Segment " << seg.Id() << std::endl;
std::cout << " orthogonal to Slave Segment " << sseg.Id() << std::endl;
#endif
if (IsTwoDimensional())
{
// get the local node id of snode on sseg
int lid = sseg.GetLocalNodeId(snode.Id());
if (lid<0)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::ProjectNodetoSegment_Orthogonal_to_Slave:\n"
<< "***ERR*** local node id could not be found\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// get coordinate of local node lid
double lidxi;
sseg.LocalCoordinatesOfNode(lid,&lidxi);
// build tangent vector in xi
double g[2];
sseg.Metric(&lidxi,g,NULL);
// we do a newton iteration for the projection coordinates xi
// set starting value to the middle of the segment
double eta = 0.0;
int i = 0;
double F=0.0,dF=0.0,deta=0.0;
for (i=0; i<10; ++i)
{
F = evaluate_F_2D_SegmentOrthogonal_to_g(snode,seg,eta,gap,g);
if (abs(F) < 1.0e-10) break;
dF = evaluate_gradF_2D_SegmentOrthogonal_to_g(snode,seg,eta,g);
deta = (-F)/dF;
eta += deta;
}
if (abs(F)>1.0e-10)
{
if (OutLevel()>3)
std::cout << "MOERTEL: ***WRN*** MOERTEL::Projector::ProjectNodetoSegment_Orthogonal_to_Slave:\n"
<< "MOERTEL: ***WRN*** Newton iteration failed to converge\n"
<< "MOERTEL: ***WRN*** #iterations = " << i << std::endl
<< "MOERTEL: ***WRN*** F(eta) = " << F << " gradF(eta) = " << dF << " eta = " << eta << " delta(eta) = " << deta << "\n"
<< "MOERTEL: ***WRN*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
}
#if 0
std::cout << "#iterations = " << i << " F = " << F << " eta = " << eta << std::endl;
#endif
xi[0] = eta;
return true;
}
else
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::ProjectNodetoSegment_Orthogonal_to_Slave:\n"
<< "***ERR*** 3D projection not impl.\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
return true;
}
/*----------------------------------------------------------------------*
| mwgee 07/05|
| modded by gah 07/2010 |
*----------------------------------------------------------------------*/
bool MOERTEL::Projector::ProjectNodetoSegment_NodalNormal(MOERTEL::Node& node,
MOERTEL::Segment& seg, double xi[], double &gap)
{
bool ok = true;
// 2D version of the problem
if (IsTwoDimensional())
{
#if 0
std::cout << "----- Projector: Node " << node.Id() << " Segment " << seg.Id() << std::endl;
std::cout << "Segment\n" << seg;
MOERTEL::Node** nodes = seg.Nodes();
std::cout << *nodes[0];
std::cout << *nodes[1];
#endif
// we do a newton iteration for the projection coordinates xi
// set starting value to the middle of the segment
double eta = 0.0;
int i = 0;
double F=0.0,dF=0.0,deta=0.0;
for (i=0; i<10; ++i)
{
F = evaluate_F_2D_NodalNormal(node,seg,eta,gap);
if (abs(F) < 1.0e-10) break;
dF = evaluate_gradF_2D_NodalNormal(node,seg,eta);
deta = (-F)/dF;
eta += deta;
}
if (abs(F)>1.0e-9)
{
ok = false;
if (OutLevel()>3)
std::cout << "MOERTEL: ***WRN*** MOERTEL::Projector::ProjectNodetoSegment_NodalNormal:\n"
<< "MOERTEL: ***WRN*** Newton iteration failed to converge\n"
<< "MOERTEL: ***WRN*** #iterations = " << i << std::endl
<< "MOERTEL: ***WRN*** F(eta) = " << F << " gradF(eta) = "
<< dF << " eta = " << eta << " delta(eta) = " << deta << "\n"
<< "MOERTEL: ***WRN*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
}
#if 0
std::cout << "#iterations = " << i << " F = " << F << " eta = " << eta << std::endl;
#endif
xi[0] = eta;
return ok;
}
// 3D version of the problem
else
{
#if 0
std::cout << "----- Projector: Node " << node.Id() << " Segment " << seg.Id() << std::endl;
std::cout << "Segment " << seg;
MOERTEL::Node** nodes = seg.Nodes();
std::cout << *nodes[0];
std::cout << *nodes[1];
std::cout << *nodes[2];
#endif
// we do a newton iteration for the projection coordinates xi
// set starting value to the middle of the segment
double eta[2];
if (seg.Nnode()==3)
eta[0] = eta[1] = 1./3.;
else
eta[0] = eta[1] = 0.;
double alpha = 0.0;
int i=0;
double F[3], dF[3][3], deta[3];
double eps;
for (i=0; i<30; ++i)
{
evaluate_FgradF_3D_NodalNormal(F,dF,node,seg,eta,alpha,gap);
eps = MOERTEL::dot(F,F,3);
if (eps < 1.0e-10) break;
// std::cout << eps << std::endl;
MOERTEL::solve33(dF,deta,F);
eta[0] -= deta[0];
eta[1] -= deta[1];
alpha -= deta[2];
}
if (eps>1.0e-10)
{
ok = false;
if (OutLevel()>3)
std::cout << "MOERTEL: ***WRN*** MOERTEL::Projector::ProjectNodetoSegment_NodalNormal:\n"
<< "MOERTEL: ***WRN*** 3D Newton iteration failed to converge\n"
<< "MOERTEL: ***WRN*** #iterations = " << i << std::endl
<< "MOERTEL: ***WRN*** eps = " << eps << " eta[3] = " << eta[0] << "/" << eta[1] << "/" << alpha << "\n"
<< "MOERTEL: ***WRN*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
}
#if 0
if (i>10)
std::cout << "#iterations = " << i << " eps = " << eps << " eta = " << eta[0] << "/" << eta[1] << std::endl;
#endif
xi[0] = eta[0];
xi[1] = eta[1];
} //
return ok;
}
/*----------------------------------------------------------------------*
| mwgee 07/05|
| 2D case: |
| this method evaluates the function |
| gradF(eta) = |
| ( Ni,eta * xis ) * ( Nj nyjs ) |
| + ( Ni * xis - xm ) * ( Nj,eta * nyjs) |
| - ( Ni,eta * yis ) * ( Nj nxjs ) |
| - ( Ni * yis - ym ) * ( Nj,eta * nxjs) |
| with Ni,eta derivative of shape functions of segment |
| Ni,Nj shape functions of segment |
| xis,yis nodal coords of segment's nodes i (slave side) |
| xm,ym nodal coords of master node |
| nxjs,nyjs outward normals of node j (slave side) |
*----------------------------------------------------------------------*/
double MOERTEL::Projector::evaluate_gradF_2D_SegmentNormal(MOERTEL::Node& node,
MOERTEL::Segment& seg,
double eta)
{
// check the type of function on the segment
// Here, we need 1D functions set as function id 0
MOERTEL::Function::FunctionType type = seg.FunctionType(0);
if (type != MOERTEL::Function::func_Linear1D)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_gradF_2D_SegmentNormal:\n"
<< "***ERR*** function is of wrong type\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// evaluate function and derivatives of the first function set on segment at eta
int nsnode = seg.Nnode();
double val[100];
double deriv[200];
seg.EvaluateFunction(0,&eta,val,nsnode,deriv);
// several intermediate data:
// Nx = Ni * xi
// Nxeta = Ni,eta * xi
// NN = Nj * nj
// NNeta = Nj,eta * nj
// get nodal coords and normals of nodes and interpolate them
double Nx[2]; Nx[0] = Nx[1] = 0.0;
double Nxeta[2]; Nxeta[0] = Nxeta[1] = 0.0;
double NN[2]; NN[0] = NN[1] = 0.0;
double NNeta[2]; NNeta[0] = NNeta[1] = 0.0;
MOERTEL::Node** snodes = seg.Nodes();
if (!snodes)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_gradF_2D_SegmentNormal:\n"
<< "***ERR*** segment " << seg.Id() << " ptr to it's nodes is zero\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
for (int i=0; i<nsnode; ++i)
{
const double* X = snodes[i]->X();
Nx[0] += val[i]*X[0];
Nx[1] += val[i]*X[1];
Nxeta[0] += deriv[i]*X[0];
Nxeta[1] += deriv[i]*X[1];
const double* N = snodes[i]->N();
NN[0] += val[i]*N[0];
NN[1] += val[i]*N[1];
NNeta[0] += deriv[i]*N[0];
NNeta[1] += deriv[i]*N[1];
}
// get master node coords
const double* xm = node.X();
// calculate gradF
double gradF = Nxeta[0]*NN[1] + (Nx[0] - xm[0])*NNeta[1]
- Nxeta[1]*NN[0] - (Nx[1] - xm[1])*NNeta[0];
return gradF;
}
/*----------------------------------------------------------------------*
| mwgee 07/05|
| modded gah 07/2010 |
| 2D case: |
| this function evaluates the function |
| F(eta) = ( Ni * xim - xs ) cross ns , |
| with Ni shape functions of segment |
| xim nodal coords of segment's nodes (master side) |
| xs nodal coords of node (slave side) |
| ns outward normal of node (slave side) |
*----------------------------------------------------------------------*/
double MOERTEL::Projector::evaluate_F_2D_NodalNormal(MOERTEL::Node& node,
MOERTEL::Segment& seg, double eta, double &gap)
{
// check the type of function on the segment
// Here, we need 1D functions set as function id 0
MOERTEL::Function::FunctionType type = seg.FunctionType(0);
if (type != MOERTEL::Function::func_Linear1D)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_F_2D_NodalNormal:\n"
<< "***ERR*** function is of wrong type\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// evaluate the first function set on segment at eta
int nmnode = seg.Nnode();
double val[100];
seg.EvaluateFunction(0,&eta,val,nmnode,NULL);
// get nodal coords of nodes and interpolate them
double Nx[2];
Nx[0] = Nx[1] = 0.0;
MOERTEL::Node** mnodes = seg.Nodes();
if (!mnodes)
{
std::stringstream oss;
oss << "***ERR*** MOERTEL::Projector::evaluate_F_2D_NodalNormal:\n"
<< "***ERR*** segment " << seg.Id() << " ptr to it's nodes is zero\n"
<< "***ERR*** file/line: " << __FILE__ << "/" << __LINE__ << "\n";
throw ReportError(oss);
}
// Here, Nx[0] and Nx[1] are the coordinates of the guess at the root
for (int i=0; i<nmnode; ++i)
{
const double* X = mnodes[i]->X();
Nx[0] += val[i]*X[0];
Nx[1] += val[i]*X[1];
}
// subtract xs (Coordinates of the slave node)
const double* X = node.X();
Nx[0] -= X[0];
Nx[1] -= X[1];
// get the normal of node
const double* n = node.N();
// calculate F
double F = Nx[0]*n[1] - Nx[1]*n[0];
gap = Nx[0] * n[0] + Nx[1] * n[1];
// Do we need to divide by the length of the normal??? GAH
//
// gap = (Nx[0] * n[0] + Nx[1] * n[1])
// / sqrt(n[0] * n[0] + n[1] * n[1]); // ||gap|| cos theta
#if 0
std::cout << "node " << node.Id() << " seg " << seg.Id() << " n[0] " << n[0] << " n[1] " << n[1] << std::endl;
std::cout << "X[0] " << X[0] << " X[1] " << X[1] << std::endl;
std::cout << "Nx[0] " << Nx[0] << " Nx[1] " << Nx[1] << " gap " << gap << std::endl;
std::cout << "norm " << sqrt(n[0] * n[0] + n[1] * n[1]) << std::endl;
#endif
return F;
}