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IFEM/src/ASM/ASMs3D.C
kmo 59d9fdc990 Added output of projected secondary solution variables to VTF 
git-svn-id: http://svn.sintef.no/trondheim/IFEM/trunk@906 e10b68d5-8a6e-419e-a041-bce267b0401d
2015-07-09 09:42:48 +02:00

1996 lines
51 KiB
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// $Id$
//==============================================================================
//!
//! \file ASMs3D.C
//!
//! \date Dec 10 2008
//!
//! \author Knut Morten Okstad / SINTEF
//!
//! \brief Driver for assembly of structured 3D spline FE models.
//!
//==============================================================================
#include "GoTools/geometry/ObjectHeader.h"
#include "GoTools/trivariate/SplineVolume.h"
#include "GoTools/trivariate/VolumeInterpolator.h"
#include "ASMs3D.h"
#include "TimeDomain.h"
#include "FiniteElement.h"
#include "GlobalIntegral.h"
#include "IntegrandBase.h"
#include "CoordinateMapping.h"
#include "GaussQuadrature.h"
#include "ElementBlock.h"
#include "Utilities.h"
#include "Profiler.h"
#include "Vec3Oper.h"
#include <ctype.h>
#include <fstream>
ASMs3D::ASMs3D (const char* fName, bool checkRHS, unsigned char n_f)
: ASMstruct(3,3,n_f), svol(0), swapW(false)
{
if (fName)
{
std::cout <<"\nReading patch file "<< fName << std::endl;
std::ifstream is(fName);
if (!is.good())
std::cerr <<" *** ASMs3D: Failure opening patch file"<< std::endl;
else if (this->read(is) && checkRHS)
this->checkRightHandSystem();
}
}
ASMs3D::ASMs3D (std::istream& is, bool checkRHS, unsigned char n_f)
: ASMstruct(3,3,n_f), svol(0), swapW(false)
{
if (this->read(is) && checkRHS)
this->checkRightHandSystem();
}
bool ASMs3D::read (std::istream& is)
{
if (svol) delete svol;
Go::ObjectHeader head;
svol = new Go::SplineVolume;
is >> head >> *svol;
// Eat white-space characters to see if there is more data to read
char c;
while (is.get(c))
if (!isspace(c))
{
is.putback(c);
break;
}
if (!is.good() && !is.eof())
{
std::cerr <<" *** ASMs3D::read: Failure reading spline data"<< std::endl;
delete svol;
svol = 0;
return false;
}
else if (svol->dimension() < 3)
{
std::cerr <<" *** ASMs3D::read: Invalid spline volume patch, dim="
<< svol->dimension() << std::endl;
delete svol;
svol = 0;
return false;
}
geo = svol;
return true;
}
bool ASMs3D::write (std::ostream& os) const
{
if (!svol) return false;
os <<"700 1 0 0\n";
os << *svol;
return os.good();
}
void ASMs3D::clear ()
{
// Erase spline data
if (svol) delete svol;
svol = 0;
geo = 0;
// Erase the FE data
nodeInd.clear();
ASMbase::clear();
}
bool ASMs3D::checkRightHandSystem ()
{
if (!svol) return false;
// Evaluate the spline volume at its center
RealArray u(1,0.5*(svol->startparam(0) + svol->endparam(0)));
RealArray v(1,0.5*(svol->startparam(1) + svol->endparam(1)));
RealArray w(1,0.5*(svol->startparam(2) + svol->endparam(2)));
RealArray X(3), dXdu(3), dXdv(3), dXdw(3);
svol->gridEvaluator(u,v,w,X,dXdu,dXdv,dXdw);
// Check that |J| = (dXdu x dXdv) * dXdw > 0.0
if (Vec3(dXdu,dXdv) * dXdw > 0.0) return false;
// This patch has a negative Jacobian determinant. Probably it is modelled
// in a left-hand-system. Swap the w-parameter direction to correct for this.
svol->reverseParameterDirection(2);
std::cout <<"\tSwapped."<< std::endl;
return swapW = true;
}
bool ASMs3D::refine (int dir, const RealArray& xi)
{
if (!svol || dir < 0 || dir > 2 || xi.empty()) return false;
if (xi.front() < 0.0 || xi.back() > 1.0) return false;
RealArray extraKnots;
RealArray::const_iterator uit = svol->basis(dir).begin();
double ucurr, uprev = *(uit++);
while (uit != svol->basis(dir).end())
{
ucurr = *(uit++);
if (ucurr > uprev)
for (size_t i = 0; i < xi.size(); i++)
if (i > 0 && xi[i] < xi[i-1])
return false;
else
extraKnots.push_back(ucurr*xi[i] + uprev*(1.0-xi[i]));
uprev = ucurr;
}
svol->insertKnot(dir,extraKnots);
return true;
}
bool ASMs3D::uniformRefine (int dir, int nInsert)
{
if (!svol || dir < 0 || dir > 2 || nInsert < 1) return false;
RealArray extraKnots;
RealArray::const_iterator uit = svol->basis(dir).begin();
double ucurr, uprev = *(uit++);
while (uit != svol->basis(dir).end())
{
ucurr = *(uit++);
if (ucurr > uprev)
for (int i = 0; i < nInsert; i++)
{
double xi = (double)(i+1)/(double)(nInsert+1);
extraKnots.push_back(ucurr*xi + uprev*(1.0-xi));
}
uprev = ucurr;
}
svol->insertKnot(dir,extraKnots);
return true;
}
bool ASMs3D::raiseOrder (int ru, int rv, int rw)
{
if (!svol) return false;
svol->raiseOrder(ru,rv,rw);
return true;
}
bool ASMs3D::generateFEMTopology ()
{
if (!svol) return false;
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
if (!nodeInd.empty())
{
if (nodeInd.size() == (size_t)n1*n2*n3) return true;
std::cerr <<" *** ASMs3D::generateFEMTopology: Inconsistency between the"
<<" number of FE nodes "<< nodeInd.size()
<<"\n and the number of spline coefficients "<< n1*n2*n3
<<" in the patch."<< std::endl;
return false;
}
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
#ifdef SP_DEBUG
std::cout <<"numCoefs: "<< n1 <<" "<< n2 <<" "<< n3;
std::cout <<"\norder: "<< p1 <<" "<< p2 <<" "<< p3;
for (int d = 0; d < 3; d++)
{
std::cout <<"\nd"<< char('u'+d) <<':';
for (int i = 0; i < svol->numCoefs(d); i++)
std::cout <<' '<< svol->knotSpan(d,i);
}
std::cout << std::endl;
#endif
// Consistency checks, just to be fool-proof
if (n1 < 2 || n2 < 2 || n3 < 2) return false;
if (p1 < 1 || p1 < 1 || p3 < 1) return false;
if (p1 > n1 || p2 > n2 || p3 > n3) return false;
MLGE.resize((n1-p1+1)*(n2-p2+1)*(n3-p3+1),0);
MLGN.resize(n1*n2*n3);
MNPC.resize(MLGE.size());
nodeInd.resize(MLGN.size());
int iel = 0;
int inod = 0;
for (int i3 = 1; i3 <= n3; i3++)
for (int i2 = 1; i2 <= n2; i2++)
for (int i1 = 1; i1 <= n1; i1++)
{
nodeInd[inod].I = i1-1;
nodeInd[inod].J = i2-1;
nodeInd[inod].K = i3-1;
if (i1 >= p1 && i2 >= p2 && i3 >= p3)
{
if (svol->knotSpan(0,i1-1) > 0.0)
if (svol->knotSpan(1,i2-1) > 0.0)
if (svol->knotSpan(2,i3-1) > 0.0)
{
MLGE[iel] = ++gEl; // global element number over all patches
MNPC[iel].resize(p1*p2*p3,0);
int lnod = 0;
for (int j3 = p3-1; j3 >= 0; j3--)
for (int j2 = p2-1; j2 >= 0; j2--)
for (int j1 = p1-1; j1 >= 0; j1--)
MNPC[iel][lnod++] = inod - n1*n2*j3 - n1*j2 - j1;
}
iel++;
}
MLGN[inod++] = ++gNod; // global node number over all patches
}
#ifdef SP_DEBUG
std::cout <<"NEL = "<< iel <<" NNOD = "<< inod << std::endl;
#endif
return true;
}
int ASMs3D::Edge::next ()
{
int ret = icnod;
icnod += incr;
return ret;
}
int ASMs3D::Face::next ()
{
int ret = isnod;
isnod += incrI;
if (++indxI >= nnodI-1)
{
indxI = 1;
isnod += incrJ - incrI*(nnodI-2);
}
return ret;
}
int ASMs3D::BlockNodes::next ()
{
int ret = iinod;
iinod += inc[0];
if (++indxI >= nnodI-1)
{
indxI = 1;
iinod += inc[1] - inc[0]*(nnodI-2);
if (++indxJ >= nnodJ-1)
{
indxJ = 1;
iinod += inc[2] - inc[1]*(nnodJ-2);
}
}
return ret;
}
bool ASMs3D::assignNodeNumbers (BlockNodes& nodes, int basis)
{
int n1, n2, n3;
if (!this->getSize(n1,n2,n3,basis))
return false;
int m1 = 0, m2 = 0, m3 = 0;
if (basis > 0)
if (!this->getSize(m1,m2,m3,3-basis))
return false;
if (MLGN.size() != (size_t)(n1*n2*n3+m1*m2*m3)) return false;
nodes.faces[0].nnodI = nodes.faces[1].nnodI = n2;
nodes.faces[2].nnodI = nodes.faces[3].nnodI = n1;
nodes.faces[4].nnodI = nodes.faces[5].nnodI = n1;
nodes.nnodI = n1;
nodes.nnodJ = n2;
if (nodes.inc[0] == 0 || nodes.inc[1] == 0 || nodes.inc[2] == 0)
{
nodes.inc[0] = 1;
nodes.inc[1] = n1-2;
nodes.inc[2] = (n1-2)*(n2-2);
}
int inod = basis > 1 ? m1*m2*m3 : 0;
for (int k = 1; k <= n3; k++)
for (int j = 1; j <= n2; j++)
for (int i = 1; i <= n1; i++, inod++)
if (k == 1)
{
if (j == 1)
{
if (i == 1)
MLGN[inod] = nodes.ibnod[0];
else if (i == n1)
MLGN[inod] = nodes.ibnod[1];
else
MLGN[inod] = nodes.edges[0].next();
}
else if (j == n2)
{
if (i == 1)
MLGN[inod] = nodes.ibnod[2];
else if (i == n1)
MLGN[inod] = nodes.ibnod[3];
else
MLGN[inod] = nodes.edges[1].next();
}
else
{
if (i == 1)
MLGN[inod] = nodes.edges[4].next();
else if (i == n1)
MLGN[inod] = nodes.edges[5].next();
else
MLGN[inod] = nodes.faces[4].next();
}
}
else if (k == n3)
{
if (j == 1)
{
if (i == 1)
MLGN[inod] = nodes.ibnod[4];
else if (i == n1)
MLGN[inod] = nodes.ibnod[5];
else
MLGN[inod] = nodes.edges[2].next();
}
else if (j == n2)
{
if (i == 1)
MLGN[inod] = nodes.ibnod[6];
else if (i == n1)
MLGN[inod] = nodes.ibnod[7];
else
MLGN[inod] = nodes.edges[3].next();
}
else
{
if (i == 1)
MLGN[inod] = nodes.edges[6].next();
else if (i == n1)
MLGN[inod] = nodes.edges[7].next();
else
MLGN[inod] = nodes.faces[5].next();
}
}
else
{
if (j == 1)
{
if (i == 1)
MLGN[inod] = nodes.edges[8].next();
else if (i == n1)
MLGN[inod] = nodes.edges[9].next();
else
MLGN[inod] = nodes.faces[2].next();
}
else if (j == n2)
{
if (i == 1)
MLGN[inod] = nodes.edges[10].next();
else if (i == n1)
MLGN[inod] = nodes.edges[11].next();
else
MLGN[inod] = nodes.faces[3].next();
}
else
{
if (i == 1)
MLGN[inod] = nodes.faces[0].next();
else if (i == n1)
MLGN[inod] = nodes.faces[1].next();
else
MLGN[inod] = nodes.next();
}
}
#if SP_DEBUG > 1
if (basis > 0) std::cout <<"\nBasis "<< basis <<":";
for (int i = inod-n1*n2*n3; i < inod; i++)
std::cout <<"\nNode "<< i+1 <<"\t: "
<< nodeInd[i].I <<" "<< nodeInd[i].J <<" "<< nodeInd[i].K
<<"\tglobal no. "<< MLGN[i];
std::cout << std::endl;
#endif
return true;
}
bool ASMs3D::connectPatch (int face, ASMs3D& neighbor, int nface, int norient)
{
if (swapW && face > 4) // Account for swapped parameter direction
face = 11-face;
if (neighbor.swapW && face > 4) // Account for swapped parameter direction
nface = 11-nface;
return this->connectBasis(face,neighbor,nface,norient);
}
bool ASMs3D::connectBasis (int face, ASMs3D& neighbor, int nface, int norient,
int basis, int slave, int master)
{
// Set up the slave node numbers for this volume patch
int n1, n2, n3;
if (!this->getSize(n1,n2,n3,basis)) return false;
int node = slave+1, i1 = 0, i2 = 0;
switch (face)
{
case 2: // Positive I-direction
node += n1-1;
case 1: // Negative I-direction
i1 = n1;
n1 = n2;
n2 = n3;
break;
case 4: // Positive J-direction
node += n1*(n2-1);
case 3: // Negative J-direction
i2 = n1*(n2-1);
i1 = 1;
n2 = n3;
break;
case 6: // Positive K-direction
node += n1*n2*(n3-1);
case 5: // Negative K-direction
i1 = 1;
break;
default:
std::cerr <<" *** ASMs3D::connectPatch: Invalid slave face "
<< face << std::endl;
return false;
}
int i, j;
IntMat slaveNodes(n1,IntVec(n2,0));
for (j = 0; j < n2; j++, node += i2)
for (i = 0; i < n1; i++, node += i1)
slaveNodes[i][j] = node;
// Set up the master node numbers for the neighboring volume patch
if (!neighbor.getSize(n1,n2,n3,basis)) return false;
node = master+1; i1 = i2 = 0;
switch (nface)
{
case 2: // Positive I-direction
node += n1-1;
case 1: // Negative I-direction
i1 = n1;
n1 = n2;
n2 = n3;
break;
case 4: // Positive J-direction
node += n1*(n2-1);
case 3: // Negative J-direction
i2 = n1*(n2-1);
i1 = 1;
n2 = n3;
break;
case 6: // Positive K-direction
node += n1*n2*(n3-1);
case 5: // Negative K-direction
i1 = 1;
break;
default:
std::cerr <<" *** ASMs3D::connectPatch: Invalid master face "
<< nface << std::endl;
return false;
}
if (norient < 0 || norient > 7)
{
std::cerr <<" *** ASMs3D::connectPatch: Orientation flag "
<< norient <<" is out of range [0,7]"<< std::endl;
return false;
}
int m1 = slaveNodes.size();
int m2 = slaveNodes.front().size();
if (norient < 4 ? (n1 != m1 || n2 != m2) : (n2 != m1 || n1 != m2))
{
std::cerr <<" *** ASMs3D::connectPatch: Non-matching faces, sizes "
<< n1 <<","<< n2 <<" and "<< m1 <<","<< m2 << std::endl;
return false;
}
const double xtol = 1.0e-4;
for (j = 0; j < n2; j++, node += i2)
for (i = 0; i < n1; i++, node += i1)
{
int k = i, l = j;
switch (norient)
{
case 1: k = i ; l = n2-j-1; break;
case 2: k = n1-i-1; l = j ; break;
case 3: k = n1-i-1; l = n2-j-1; break;
case 4: k = j ; l = i ; break;
case 5: k = j ; l = n1-i-1; break;
case 6: k = n2-j-1; l = i ; break;
case 7: k = n2-j-1; l = n1-i-1; break;
default: k = i ; l = j ;
}
if (!neighbor.getCoord(node).equal(this->getCoord(slaveNodes[k][l]),xtol))
{
std::cerr <<" *** ASMs3D::connectPatch: Non-matching nodes "
<< node <<": "<< neighbor.getCoord(node)
<<"\n and "
<< slaveNodes[k][l] <<": "<< this->getCoord(slaveNodes[k][l])
<< std::endl;
return false;
}
else
ASMbase::collapseNodes(neighbor.MLGN[node-1],MLGN[slaveNodes[k][l]-1]);
}
return true;
}
void ASMs3D::closeFaces (int dir, int basis, int master)
{
int n1, n2, n3;
if (basis < 1) basis = 1;
if (!this->getSize(n1,n2,n3,basis)) return;
switch (dir)
{
case 1: // Faces are closed in I-direction
for (int i3 = 1; i3 <= n3; i3++)
for (int i2 = 1; i2 <= n2; i2++, master += n1)
this->makePeriodic(master,master+n1-1);
break;
case 2: // Faces are closed in J-direction
for (int i3 = 1; i3 <= n3; i3++, master += n1*(n2-1))
for (int i1 = 1; i1 <= n1; i1++, master++)
this->makePeriodic(master,master+n1*(n2-1));
break;
case 3: // Faces are closed in K-direction
for (int i2 = 1; i2 <= n2; i2++)
for (int i1 = 1; i1 <= n1; i1++, master++)
this->makePeriodic(master,master+n1*n2*(n3-1));
break;
}
}
void ASMs3D::constrainFace (int dir, int dof, int code)
{
int n1, n2, n3, node = 1;
if (!this->getSize(n1,n2,n3,1)) return;
if (swapW) // Account for swapped parameter direction
if (dir == 3 || dir == -3) dir = -dir;
switch (dir)
{
case 1: // Right face (positive I-direction)
node += n1-1;
case -1: // Left face (negative I-direction)
for (int i3 = 1; i3 <= n3; i3++)
for (int i2 = 1; i2 <= n2; i2++, node += n1)
this->prescribe(node,dof,code);
break;
case 2: // Back face (positive J-direction)
node += n1*(n2-1);
case -2: // Front face (negative J-direction)
for (int i3 = 1; i3 <= n3; i3++, node += n1*(n2-1))
for (int i1 = 1; i1 <= n1; i1++, node++)
this->prescribe(node,dof,code);
break;
case 3: // Top face (positive K-direction)
node += n1*n2*(n3-1);
case -3: // Bottom face (negative K-direction)
for (int i2 = 1; i2 <= n2; i2++)
for (int i1 = 1; i1 <= n1; i1++, node++)
this->prescribe(node,dof,code);
break;
}
}
void ASMs3D::constrainEdge (int lEdge, int dof, int code)
{
int n1, n2, n3, n, node = 1, inc = 1;
if (!this->getSize(n1,n2,n3,1)) return;
if (swapW && lEdge <= 8) // Account for swapped parameter direction
lEdge += (lEdge-1)%4 < 2 ? 2 : -2;
if (lEdge > 8)
{
inc = n1*n2;
n = n3;
}
else if (lEdge > 4)
{
inc = n1;
n = n2;
}
else
n = n1;
switch (lEdge)
{
case 6:
case 10:
node = n1;
break;
case 2:
case 12:
node = n1*(n2-1) + 1;
break;
case 11:
node = n1*n2;
break;
case 3:
case 7:
node = n1*n2*(n3-1) + 1;
break;
case 8:
node = n1*(n2*(n3-1) + 1);
break;
case 4:
node = n1*(n2*n3-1) + 1;
break;
}
for (int i = 0; i < n; i++, node += inc)
this->prescribe(node,dof,code);
}
void ASMs3D::constrainLine (int fdir, int ldir, double xi, int dof, int code)
{
if (xi < 0.0 || xi > 1.0) return;
int n1, n2, n3, node = 1;
if (!this->getSize(n1,n2,n3,1)) return;
if (swapW) // Account for swapped parameter direction
if (fdir == 3 || fdir == -3) fdir = -fdir;
switch (fdir)
{
case 1: // Right face (positive I-direction)
node += n1-1;
case -1: // Left face (negative I-direction)
if (ldir == 2)
{
// Line goes in J-direction
node += n1*n2*int(0.5+(n3-1)*(swapW ? 1.0-xi : xi));
for (int i2 = 1; i2 <= n2; i2++, node += n1)
this->prescribe(node,dof,code);
}
else if (ldir == 3)
{
// Line goes in K-direction
node += n1*int(0.5+(n2-1)*xi);
for (int i3 = 1; i3 <= n3; i3++, node += n1*n2)
this->prescribe(node,dof,code);
}
break;
case 2: // Back face (positive J-direction)
node += n1*(n2-1);
case -2: // Front face (negative J-direction)
if (ldir == 1)
{
// Line goes in I-direction
node += n1*n2*int(0.5+(n3-1)*(swapW ? 1.0-xi : xi));
for (int i1 = 1; i1 <= n1; i1++, node++)
this->prescribe(node,dof,code);
}
else if (ldir == 3)
{
// Line goes in K-direction
node += int(0.5+(n1-1)*xi);
for (int i3 = 1; i3 <= n3; i3++, node += n1*n2)
this->prescribe(node,dof,code);
}
break;
case 3: // Top face (positive K-direction)
node += n1*n2*(n3-1);
case -3: // Bottom face (negative K-direction)
if (ldir == 1)
{
// Line goes in I-direction
node += n1*int(0.5+(n2-1)*xi);
for (int i1 = 1; i1 <= n1; i1++, node++)
this->prescribe(node,dof,code);
}
else if (ldir == 2)
{
// Line goes in J-direction
node += int(0.5+(n1-1)*xi);
for (int i2 = 1; i2 <= n2; i2++, node += n1)
this->prescribe(node,dof,code);
}
break;
}
}
void ASMs3D::constrainCorner (int I, int J, int K, int dof, int code)
{
int n1, n2, n3;
if (!this->getSize(n1,n2,n3,1)) return;
if (swapW) // Account for swapped parameter direction
K = -K;
int node = 1;
if (I > 0) node += n1-1;
if (J > 0) node += n1*(n2-1);
if (K > 0) node += n1*n2*(n3-1);
this->prescribe(node,dof,code);
}
void ASMs3D::constrainNode (double xi, double eta, double zeta,
int dof, int code)
{
if (xi < 0.0 || xi > 1.0) return;
if (eta < 0.0 || eta > 1.0) return;
if (zeta < 0.0 || zeta > 1.0) return;
if (swapW) // Account for swapped parameter direction
zeta = 1.0-zeta;
int n1, n2, n3;
if (!this->getSize(n1,n2,n3,1)) return;
int node = 1;
if (xi > 0.0) node += int(0.5+(n1-1)*xi);
if (eta > 0.0) node += n1*int(0.5+(n2-1)*eta);
if (zeta > 0.0) node += n1*n2*int(0.5+(n3-1)*zeta);
this->prescribe(node,dof,code);
}
#define DERR -999.99
double ASMs3D::getParametricVolume (int iel) const
{
#ifdef INDEX_CHECK
if (iel < 1 || (size_t)iel > MNPC.size())
{
std::cerr <<" *** ASMs3D::getParametricVolume: Element index "<< iel
<<" out of range [1,"<< MNPC.size() <<"]."<< std::endl;
return DERR;
}
#endif
if (MNPC[iel-1].empty())
return 0.0;
int inod1 = MNPC[iel-1].back();
#ifdef INDEX_CHECK
if (inod1 < 0 || (size_t)inod1 >= nodeInd.size())
{
std::cerr <<" *** ASMs3D::getParametricVolume: Node index "<< inod1
<<" out of range [0,"<< nodeInd.size() <<">."<< std::endl;
return DERR;
}
#endif
double du = svol->knotSpan(0,nodeInd[inod1].I);
double dv = svol->knotSpan(1,nodeInd[inod1].J);
double dw = svol->knotSpan(2,nodeInd[inod1].K);
return du*dv*dw;
}
double ASMs3D::getParametricArea (int iel, int dir) const
{
#ifdef INDEX_CHECK
if (iel < 1 || (size_t)iel > MNPC.size())
{
std::cerr <<" *** ASMs3D::getParametricArea: Element index "<< iel
<<" out of range [1,"<< MNPC.size() <<"]."<< std::endl;
return DERR;
}
#endif
if (MNPC[iel-1].empty())
return 0.0;
int inod1 = MNPC[iel-1].back();
#ifdef INDEX_CHECK
if (inod1 < 0 || (size_t)inod1 >= nodeInd.size())
{
std::cerr <<" *** ASMs3D::getParametricArea: Node index "<< inod1
<<" out of range [0,"<< nodeInd.size() <<">."<< std::endl;
return DERR;
}
#endif
const int ni = nodeInd[inod1].I;
const int nj = nodeInd[inod1].J;
const int nk = nodeInd[inod1].K;
switch (dir)
{
case 1: return svol->knotSpan(1,nj)*svol->knotSpan(2,nk);
case 2: return svol->knotSpan(0,ni)*svol->knotSpan(2,nk);
case 3: return svol->knotSpan(0,ni)*svol->knotSpan(1,nj);
}
std::cerr <<" *** ASMs3D::getParametricArea: Invalid face direction "
<< dir << std::endl;
return DERR;
}
int ASMs3D::coeffInd (size_t inod) const
{
#ifdef INDEX_CHECK
if (inod >= nodeInd.size())
{
std::cerr <<" *** ASMs3D::coeffInd: Node index "<< inod
<<" out of range [0,"<< nodeInd.size() <<">."<< std::endl;
return -1;
}
#endif
const int ni = nodeInd[inod].I;
const int nj = nodeInd[inod].J;
const int nk = nodeInd[inod].K;
return (nk*svol->numCoefs(1) + nj)*svol->numCoefs(0) + ni;
}
bool ASMs3D::getElementCoordinates (Matrix& X, int iel) const
{
#ifdef INDEX_CHECK
if (iel < 1 || (size_t)iel > MNPC.size())
{
std::cerr <<" *** ASMs3D::getElementCoordinates: Element index "<< iel
<<" out of range [1,"<< MNPC.size() <<"]."<< std::endl;
return false;
}
#endif
const IntVec& mnpc = MNPC[iel-1];
X.resize(3,mnpc.size());
RealArray::const_iterator cit = svol->coefs_begin();
for (size_t n = 0; n < mnpc.size(); n++)
{
int ip = this->coeffInd(mnpc[n])*svol->dimension();
if (ip < 0) return false;
for (size_t i = 0; i < 3; i++)
X(i+1,n+1) = *(cit+(ip+i));
}
#if SP_DEBUG > 2
std::cout <<"\nCoordinates for element "<< iel << X << std::endl;
#endif
return true;
}
void ASMs3D::getNodalCoordinates (Matrix& X) const
{
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
X.resize(3,n1*n2*n3);
RealArray::const_iterator cit = svol->coefs_begin();
size_t inod = 1;
for (int i3 = 0; i3 < n3; i3++)
for (int i2 = 0; i2 < n2; i2++)
for (int i1 = 0; i1 < n1; i1++, inod++)
{
int ip = ((i3*n2 + i2)*n1 + i1)*svol->dimension();
for (size_t i = 0; i < 3; i++)
X(i+1,inod) = *(cit+(ip+i));
}
}
Vec3 ASMs3D::getCoord (size_t inod) const
{
if (inod == 0) return Vec3();
int ip = this->coeffInd(inod-1)*svol->dimension();
if (ip < 0) return Vec3();
RealArray::const_iterator cit = svol->coefs_begin() + ip;
return Vec3(*cit,*(cit+1),*(cit+2));
}
bool ASMs3D::getSize (int& n1, int& n2, int& n3, int) const
{
if (!svol) return false;
n1 = svol->numCoefs(0);
n2 = svol->numCoefs(1);
n3 = svol->numCoefs(2);
return true;
}
/*!
\brief Computes the characteristic element length from nodal coordinates.
*/
static double getElmSize (int p1, int p2, int p3, const Matrix& X)
{
int i, j, k, id1, id2;
double value, v1, h = 1.0e12;
// Z-direction
for (i = 1; i <= p1; i++)
for (j = 0; j < p2; j++)
{
id1 = j*p1 + i;
id2 = id1 + (p3-1)*p2*p1;
value = 0.0;
for (k = 1; k <= 3; k++)
{
v1 = X(k,id2) - X(k,id1);
value += v1*v1;
}
if (value < h) h = value;
}
// Y-direction
for (i = 1; i <= p1; i++)
for (k = 0; k < p2; k++)
{
id1 = k*p2*p1 + i;
id2 = id1 + (p2-1)*p1;
value = 0.0;
for (j = 1; j <= 3; j++)
{
v1 = X(j,id2) - X(j,id1);
value += v1*v1;
}
if (value < h) h = value;
}
// X-direction
for (j = 0; j < p2; j++)
for (k = 0; k < p3; k++)
{
id1 = k*p1*p2 + j*p1 + 1;
id2 = id1 + p1 - 1;
value = 0.0;
for (i = 1; i <= 3; i++)
{
v1 = X(i,id2) - X(i,id1);
value += v1*v1;
}
if (value < h) h = value;
}
return sqrt(h);
}
void ASMs3D::extractBasis (const Go::BasisDerivs& spline,
Vector& N, Matrix& dNdu)
{
dNdu.resize(N.size(),3);
size_t jp, n = 1;
for (jp = 0; jp < N.size(); jp++, n++)
{
N (n) = spline.basisValues[jp];
dNdu(n,1) = spline.basisDerivs_u[jp];
dNdu(n,2) = spline.basisDerivs_v[jp];
dNdu(n,3) = spline.basisDerivs_w[jp];
}
}
void ASMs3D::extractBasis (const Go::BasisDerivs2& spline,
Vector& N, Matrix& dNdu, Matrix3D& d2Ndu2)
{
dNdu .resize(N.size(),3);
d2Ndu2.resize(N.size(),3,3);
size_t jp, n = 1;
for (jp = 0; jp < N.size(); jp++, n++)
{
N (n) = spline.basisValues[jp];
dNdu (n,1) = spline.basisDerivs_u[jp];
dNdu (n,2) = spline.basisDerivs_v[jp];
dNdu (n,3) = spline.basisDerivs_w[jp];
d2Ndu2(n,1,1) = spline.basisDerivs_uu[jp];
d2Ndu2(n,1,2) = d2Ndu2(n,2,1) = spline.basisDerivs_uv[jp];
d2Ndu2(n,1,3) = d2Ndu2(n,3,1) = spline.basisDerivs_uw[jp];
d2Ndu2(n,2,2) = spline.basisDerivs_vv[jp];
d2Ndu2(n,2,3) = d2Ndu2(n,3,2) = spline.basisDerivs_vw[jp];
d2Ndu2(n,3,3) = spline.basisDerivs_ww[jp];
}
}
bool ASMs3D::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time,
const LintegralVec& locInt)
{
if (!svol) return true; // silently ignore empty patches
PROFILE2("ASMs3D::integrate(I)");
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Compute parameter values of the Gauss points over the whole patch
int dir;
Matrix gpar[3];
for (dir = 0; dir < 3; dir++)
{
int pm1 = svol->order(dir) - 1;
RealArray::const_iterator uit = svol->basis(dir).begin() + pm1;
double ucurr, uprev = *(uit++);
int nCol = svol->numCoefs(dir) - pm1;
gpar[dir].resize(nGauss,nCol);
for (int j = 1; j <= nCol; uit++, j++)
{
ucurr = *uit;
for (int i = 1; i <= nGauss; i++)
gpar[dir](i,j) = 0.5*((ucurr-uprev)*xg[i-1] + ucurr+uprev);
uprev = ucurr;
}
}
// Evaluate basis function derivatives at all integration points
std::vector<Go::BasisDerivs> spline;
std::vector<Go::BasisDerivs2> spline2;
{
PROFILE2("Spline evaluation");
if (integrand.getIntegrandType() == 2)
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline2);
else
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline);
}
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int nel1 = n1 - p1 + 1;
const int nel2 = n2 - p2 + 1;
FiniteElement fe(p1*p2*p3);
Matrix dNdu, Xnod, Jac;
Matrix3D d2Ndu2, Hess;
Vec4 X;
// === Assembly loop over all elements in the patch ==========================
int iel = 1;
for (int i3 = p3; i3 <= n3; i3++)
for (int i2 = p2; i2 <= n2; i2++)
for (int i1 = p1; i1 <= n1; i1++, iel++)
{
if (MLGE[iel-1] < 1) continue; // zero-volume element
// Get element volume in the parameter space
double dV = this->getParametricVolume(iel);
if (dV < 0.0) return false; // topology error (probably logic error)
// Set up control point (nodal) coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Compute characteristic element length, if needed
if (integrand.getIntegrandType() == 2)
fe.h = getElmSize(p1,p2,p3,Xnod);
else if (integrand.getIntegrandType() == 3)
{
// --- Compute average value of basis functions over the element -----
fe.Navg.resize(p1*p2*p3,true);
double vol = 0.0;
int ip = (((i3-p3)*nGauss*nel2 + i2-p2)*nGauss*nel1 + i1-p1)*nGauss;
for (int k = 0; k < nGauss; k++, ip += nGauss*(nel2-1)*nGauss*nel1)
for (int j = 0; j < nGauss; j++, ip += nGauss*(nel1-1))
for (int i = 0; i < nGauss; i++, ip++)
{
// Fetch basis function derivatives at current integration point
extractBasis(spline[ip],fe.N,dNdu);
// Compute Jacobian determinant of coordinate mapping
// and multiply by weight of current integration point
double detJac = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu,false);
double weight = 0.125*dV*wg[i]*wg[j]*wg[k];
// Numerical quadrature
fe.Navg.add(fe.N,detJac*weight);
vol += detJac*weight;
}
// Divide by element volume
fe.Navg /= vol;
}
else if (integrand.getIntegrandType() == 4)
{
// Compute the element center
Go::Point X0;
double u0 = 0.5*(gpar[0](1,i1-p1+1) + gpar[0](nGauss,i1-p1+1));
double v0 = 0.5*(gpar[1](1,i2-p2+1) + gpar[1](nGauss,i2-p2+1));
double w0 = 0.5*(gpar[2](1,i3-p3+1) + gpar[2](nGauss,i3-p3+1));
svol->point(X0,u0,v0,w0);
X.x = X0[0];
X.y = X0[1];
X.z = X0[2];
}
// Initialize element quantities
if (!integrand.initElement(MNPC[iel-1],X,nGauss*nGauss*nGauss))
return false;
// Caution: Unless locInt is empty, we assume it points to an array of
// LocalIntegral pointers, of length at least the number of elements in
// the model (as defined by the highest number in the MLGE array).
// If the array is shorter than this, expect a segmentation fault.
LocalIntegral* elmInt = locInt.empty() ? 0 : locInt[MLGE[iel-1]-1];
// --- Integration loop over all Gauss points in each direction --------
int ip = (((i3-p3)*nGauss*nel2 + i2-p2)*nGauss*nel1 + i1-p1)*nGauss;
for (int k = 0; k < nGauss; k++, ip += nGauss*(nel2-1)*nGauss*nel1)
for (int j = 0; j < nGauss; j++, ip += nGauss*(nel1-1))
for (int i = 0; i < nGauss; i++, ip++)
{
// Parameter values of current integration point
fe.u = gpar[0](i+1,i1-p1+1);
fe.v = gpar[1](j+1,i2-p2+1);
fe.w = gpar[2](k+1,i3-p3+1);
// Fetch basis function derivatives at current integration point
if (integrand.getIntegrandType() == 2)
extractBasis(spline2[ip],fe.N,dNdu,d2Ndu2);
else
extractBasis(spline[ip],fe.N,dNdu);
// Compute Jacobian inverse of coordinate mapping and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
if (fe.detJxW == 0.0) continue; // skip singular points
// Compute Hessian of coordinate mapping and 2nd order derivatives
if (integrand.getIntegrandType() == 2)
if (!utl::Hessian(Hess,fe.d2NdX2,Jac,Xnod,d2Ndu2,dNdu))
return false;
#if SP_DEBUG > 4
std::cout <<"\niel, ip = "<< iel <<" "<< ip
<<"\nN ="<< fe.N <<"dNdX ="<< fe.dNdX << std::endl;
#endif
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= 0.125*dV*wg[i]*wg[j]*wg[k];
if (!integrand.evalInt(elmInt,fe,time,X))
return false;
}
// Finalize the element quantities
if (!integrand.finalizeElement(elmInt,time))
return false;
// Assembly of global system integral
if (!glInt.assemble(elmInt,MLGE[iel-1]))
return false;
}
return true;
}
bool ASMs3D::integrate (Integrand& integrand, int lIndex,
GlobalIntegral& glInt,
const TimeDomain& time,
const LintegralVec& locInt)
{
if (!svol) return true; // silently ignore empty patches
PROFILE2("ASMs3D::integrate(B)");
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Find the parametric direction of the face normal {-3,-2,-1, 1, 2, 3}
const int faceDir = (lIndex+1)/(lIndex%2 ? -2 : 2);
const int t1 = 1 + abs(faceDir)%3; // first tangent direction
const int t2 = 1 + t1%3; // second tangent direction
// Compute parameter values of the Gauss points over the whole patch face
Matrix gpar[3];
for (int d = 0; d < 3; d++)
if (-1-d == faceDir)
{
gpar[d].resize(1,1);
gpar[d](1,1) = svol->startparam(d);
}
else if (1+d == faceDir)
{
gpar[d].resize(1,1);
gpar[d](1,1) = svol->endparam(d);
}
else
{
int pm1 = svol->order(d) - 1;
RealArray::const_iterator uit = svol->basis(d).begin() + pm1;
double ucurr, uprev = *(uit++);
int nCol = svol->numCoefs(d) - pm1;
gpar[d].resize(nGauss,nCol);
for (int j = 1; j <= nCol; uit++, j++)
{
ucurr = *uit;
for (int i = 1; i <= nGauss; i++)
gpar[d](i,j) = 0.5*((ucurr-uprev)*xg[i-1] + ucurr+uprev);
uprev = ucurr;
}
}
// Evaluate basis function derivatives at all integration points
std::vector<Go::BasisDerivs> spline;
{
PROFILE2("Spline evaluation");
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline);
}
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int nel1 = n1 - p1 + 1;
const int nel2 = n2 - p2 + 1;
FiniteElement fe(p1*p2*p3);
fe.u = gpar[0](1,1);
fe.v = gpar[1](1,1);
fe.w = gpar[2](1,1);
Matrix dNdu, Xnod, Jac;
Vec4 X;
Vec3 normal;
// === Assembly loop over all elements on the patch face =====================
int iel = 1;
for (int i3 = p3; i3 <= n3; i3++)
for (int i2 = p2; i2 <= n2; i2++)
for (int i1 = p1; i1 <= n1; i1++, iel++)
{
if (MLGE[iel-1] < 1) continue; // zero-volume element
// Skip elements that are not on current boundary face
bool skipMe = false;
switch (faceDir)
{
case -1: if (i1 > p1) skipMe = true; break;
case 1: if (i1 < n1) skipMe = true; break;
case -2: if (i2 > p2) skipMe = true; break;
case 2: if (i2 < n2) skipMe = true; break;
case -3: if (i3 > p3) skipMe = true; break;
case 3: if (i3 < n3) skipMe = true; break;
}
if (skipMe) continue;
// Get element face area in the parameter space
double dA = this->getParametricArea(iel,abs(faceDir));
if (dA < 0.0) return false; // topology error (probably logic error)
// Set up control point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Initialize element quantities
if (!integrand.initElementBou(MNPC[iel-1])) return false;
// Define some loop control variables depending on which face we are on
int nf1, j1, j2;
switch (abs(faceDir))
{
case 1: nf1 = nel2; j2 = i3-p3; j1 = i2-p2; break;
case 2: nf1 = nel1; j2 = i3-p3; j1 = i1-p1; break;
case 3: nf1 = nel1; j2 = i2-p2; j1 = i1-p1; break;
default: nf1 = j1 = j2 = 0;
}
// Caution: Unless locInt is empty, we assume it points to an array of
// LocalIntegral pointers, of length at least the number of elements in
// the model (as defined by the highest number in the MLGE array).
// If the array is shorter than this, expect a segmentation fault.
LocalIntegral* elmInt = locInt.empty() ? 0 : locInt[MLGE[iel-1]-1];
// --- Integration loop over all Gauss points in each direction --------
int k1, k2, k3;
int ip = (j2*nGauss*nf1 + j1)*nGauss;
for (int j = 0; j < nGauss; j++, ip += nGauss*(nf1-1))
for (int i = 0; i < nGauss; i++, ip++)
{
// Parameter values of current integration point
switch (abs(faceDir)) {
case 1: k2 = i+1; k3 = j+1; k1 = 0; break;
case 2: k1 = i+1; k3 = j+1; k2 = 0; break;
case 3: k1 = i+1; k2 = j+1; k3 = 0; break;
default: k1 = k2 = k3 = 0;
}
if (gpar[0].size() > 1) fe.u = gpar[0](k1,i1-p1+1);
if (gpar[1].size() > 1) fe.v = gpar[1](k2,i2-p2+1);
if (gpar[2].size() > 1) fe.w = gpar[1](k3,i3-p3+1);
// Fetch basis function derivatives at current integration point
extractBasis(spline[ip],fe.N,dNdu);
// Compute basis function derivatives and the face normal
fe.detJxW = utl::Jacobian(Jac,normal,fe.dNdX,Xnod,dNdu,t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
if (faceDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= 0.25*dA*wg[i]*wg[j];
if (!integrand.evalBou(elmInt,fe,time,X,normal))
return false;
}
// Assembly of global system integral
if (!glInt.assemble(elmInt,MLGE[iel-1]))
return false;
}
return true;
}
bool ASMs3D::integrateEdge (Integrand& integrand, int lEdge,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) return true; // silently ignore empty patches
PROFILE2("ASMs3D::integrate(E)");
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Compute parameter values of the Gauss points along the whole patch edge
Matrix gpar[3];
for (int d = 0; d < 3; d++)
if (lEdge < d*4+1 || lEdge >= d*4+5)
{
gpar[d].resize(1,1);
if (lEdge%4 == 1)
gpar[d](1,1) = svol->startparam(d);
else if (lEdge%4 == 0)
gpar[d](1,1) = svol->endparam(d);
else if (lEdge == 6 || lEdge == 10)
gpar[d](1,1) = d == 0 ? svol->endparam(d) : svol->startparam(d);
else if (lEdge == 2 || lEdge == 11)
gpar[d](1,1) = d == 1 ? svol->endparam(d) : svol->startparam(d);
else if (lEdge == 3 || lEdge == 7)
gpar[d](1,1) = d == 2 ? svol->endparam(d) : svol->startparam(d);
}
else
{
int pm1 = svol->order(d) - 1;
RealArray::const_iterator uit = svol->basis(d).begin() + pm1;
double ucurr, uprev = *(uit++);
int nCol = svol->numCoefs(d) - pm1;
gpar[d].resize(nGauss,nCol);
for (int j = 1; j <= nCol; uit++, j++)
{
ucurr = *uit;
for (int i = 1; i <= nGauss; i++)
gpar[d](i,j) = 0.5*((ucurr-uprev)*xg[i-1] + ucurr+uprev);
uprev = ucurr;
}
}
// Evaluate basis function derivatives at all integration points
std::vector<Go::BasisDerivs> spline;
{
PROFILE2("Spline evaluation");
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline);
}
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
FiniteElement fe(p1*p2*p3);
fe.u = gpar[0](1,1);
fe.v = gpar[1](1,1);
fe.w = gpar[2](1,1);
Matrix dNdu, Xnod, Jac;
Vec4 X;
Vec3 tang;
// === Assembly loop over all elements on the patch edge =====================
int iel = 1;
for (int i3 = p3; i3 <= n3; i3++)
for (int i2 = p2; i2 <= n2; i2++)
for (int i1 = p1; i1 <= n1; i1++, iel++)
{
if (MLGE[iel-1] < 1) continue; // zero-volume element
// Skip elements that are not on current boundary edge
bool skipMe = false;
switch (lEdge)
{
case 1: if (i2 > p2 || i3 > p3) skipMe = true; break;
case 2: if (i2 < n2 || i3 > p3) skipMe = true; break;
case 3: if (i2 > p2 || i3 < n3) skipMe = true; break;
case 4: if (i2 < n2 || i3 < n3) skipMe = true; break;
case 5: if (i1 > p1 || i3 > p3) skipMe = true; break;
case 6: if (i1 < n1 || i3 > p3) skipMe = true; break;
case 7: if (i1 > p1 || i3 < n3) skipMe = true; break;
case 8: if (i1 < n1 || i3 < n3) skipMe = true; break;
case 9: if (i1 > p1 || i2 > p2) skipMe = true; break;
case 10: if (i1 < n1 || i2 > p2) skipMe = true; break;
case 11: if (i1 > p1 || i2 < n2) skipMe = true; break;
case 12: if (i1 < n1 || i2 < n2) skipMe = true; break;
}
if (skipMe) continue;
// Get element edge length in the parameter space
double dS = 0.0;
int ip = MNPC[iel-1].back();
#ifdef INDEX_CHECK
if (ip < 0 || (size_t)ip >= nodeInd.size()) return false;
#endif
if (lEdge < 5)
{
dS = svol->knotSpan(0,nodeInd[ip].I);
ip = (i1-p1)*nGauss;
}
else if (lEdge < 9)
{
dS = svol->knotSpan(1,nodeInd[ip].J);
ip = (i2-p2)*nGauss;
}
else if (lEdge < 13)
{
dS = svol->knotSpan(2,nodeInd[ip].K);
ip = (i3-p3)*nGauss;
}
// Set up control point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Initialize element quantities
if (!integrand.initElementBou(MNPC[iel-1])) return false;
// --- Integration loop over all Gauss points along the edge -----------
LocalIntegral* elmInt = 0;
for (int i = 0; i < nGauss; i++, ip++)
{
// Parameter values of current integration point
if (gpar[0].size() > 1) fe.u = gpar[0](i+1,i1-p1+1);
if (gpar[1].size() > 1) fe.v = gpar[1](i+1,i2-p2+1);
if (gpar[2].size() > 1) fe.w = gpar[1](i+1,i3-p3+1);
// Fetch basis function derivatives at current integration point
extractBasis(spline[ip],fe.N,dNdu);
// Compute basis function derivatives and the edge tang
fe.detJxW = utl::Jacobian(Jac,tang,fe.dNdX,Xnod,dNdu,1+(lEdge-1)/4);
if (fe.detJxW == 0.0) continue; // skip singular points
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= 0.5*dS*wg[i];
if (!integrand.evalBou(elmInt,fe,time,X,tang))
return false;
}
// Assembly of global system integral
if (!glInt.assemble(elmInt,MLGE[iel-1]))
return false;
}
return true;
}
int ASMs3D::evalPoint (const double* xi, double* param, Vec3& X) const
{
if (!svol) return -3;
int i;
for (i = 0; i < 3; i++)
param[i] = (1.0-xi[i])*svol->startparam(i) + xi[i]*svol->endparam(i);
Go::Point X0;
svol->point(X0,param[0],param[1],param[2]);
for (i = 0; i < 3 && i < svol->dimension(); i++)
X[i] = X0[i];
// Check if this point matches any of the control points (nodes)
Vec3 Xnod;
size_t inod = 1;
RealArray::const_iterator cit = svol->coefs_begin();
for (i = 0; cit != svol->coefs_end(); cit++, i++)
{
if (i < 3) Xnod[i] = *cit;
if (i+1 == svol->dimension())
if (X.equal(Xnod,0.001))
return inod;
else
{
inod++;
i = -1;
}
}
return 0;
}
bool ASMs3D::getGridParameters (RealArray& prm, int dir, int nSegPerSpan) const
{
if (!svol) return false;
if (nSegPerSpan < 1)
{
std::cerr <<" *** ASMs3D::getGridParameters: Too few knot-span points "
<< nSegPerSpan+1 <<" in direction "<< dir << std::endl;
return false;
}
RealArray::const_iterator uit = svol->basis(dir).begin();
double ucurr = 0.0, uprev = *(uit++);
while (uit != svol->basis(dir).end())
{
ucurr = *(uit++);
if (ucurr > uprev)
if (nSegPerSpan == 1)
prm.push_back(uprev);
else for (int i = 0; i < nSegPerSpan; i++)
{
double xg = (double)(2*i-nSegPerSpan)/(double)nSegPerSpan;
prm.push_back(0.5*(ucurr*(1.0+xg) + uprev*(1.0-xg)));
}
uprev = ucurr;
}
if (ucurr > prm.back())
prm.push_back(ucurr);
return true;
}
bool ASMs3D::getGrevilleParameters (RealArray& prm, int dir) const
{
if (!svol) return false;
const Go::BsplineBasis& basis = svol->basis(dir);
prm.resize(basis.numCoefs());
for (size_t i = 0; i < prm.size(); i++)
prm[i] = basis.grevilleParameter(i);
return true;
}
bool ASMs3D::tesselate (ElementBlock& grid, const int* npe) const
{
// Compute parameter values of the nodal points
RealArray gpar[3];
for (int dir = 0; dir < 3; dir++)
if (!this->getGridParameters(gpar[dir],dir,npe[dir]-1))
return false;
// Evaluate the spline volume at all points
size_t nx = gpar[0].size();
size_t ny = gpar[1].size();
size_t nz = gpar[2].size();
RealArray XYZ(svol->dimension()*nx*ny*nz);
svol->gridEvaluator(gpar[0],gpar[1],gpar[2],XYZ);
// Establish the block grid coordinates
size_t i, j, k, l;
grid.resize(nx,ny,nz);
for (i = j = 0; i < grid.getNoNodes(); i++, j += svol->dimension())
grid.setCoor(i,XYZ[j],XYZ[j+1],XYZ[j+2]);
// Establish the block grid topology
int n[8], ip = 0;
for (k = 1, n[2] = 0; k < nz; k++)
for (j = 1, n[1] = n[2]; j < ny; j++)
{
n[0] = n[1];
n[1] = n[0] + 1;
n[2] = n[1] + nx;
n[3] = n[1] + nx-1;
n[4] = n[0] + nx*ny;
n[5] = n[4] + 1;
n[6] = n[5] + nx;
n[7] = n[5] + nx-1;
for (i = 1; i < nx; i++)
for (l = 0; l < 8; l++)
grid.setNode(ip++,n[l]++);
}
return true;
}
void ASMs3D::scatterInd (int n1, int n2, int n3, int p1, int p2, int p3,
const int* start, IntVec& index)
{
index.reserve(p1*p2*p3);
int ip = ((start[2]-p3+1)*n2 + (start[1]-p2+1))*n1 + (start[0]-p1+1);
for (int i3 = 0; i3 < p3; i3++, ip += n1*(n2-p2))
for (int i2 = 0; i2 < p2; i2++, ip += n1-p1)
for (int i1 = 0; i1 < p1; i1++, ip++)
index.push_back(ip);
}
bool ASMs3D::evalSolution (Matrix& sField, const Vector& locSol,
const int* npe) const
{
// Compute parameter values of the result sampling points
RealArray gpar[3];
for (int dir = 0; dir < 3; dir++)
if (!this->getGridParameters(gpar[dir],dir,npe[dir]-1))
return false;
// Evaluate the primary solution at all sampling points
return this->evalSolution(sField,locSol,gpar);
}
bool ASMs3D::evalSolution (Matrix& sField, const Vector& locSol,
const RealArray* gpar, bool regular) const
{
// Evaluate the basis functions at all points
std::vector<Go::BasisPts> spline;
if (regular)
{
PROFILE2("Spline evaluation");
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline);
}
else if (gpar[0].size() == gpar[1].size() && gpar[0].size() == gpar[2].size())
{
PROFILE2("Spline evaluation");
spline.resize(gpar[0].size());
std::vector<Go::BasisPts> tmpSpline(1);
for (size_t i = 0; i < spline.size(); i++)
{
svol->computeBasisGrid(RealArray(1,gpar[0][i]),
RealArray(1,gpar[1][i]),
RealArray(1,gpar[2][i]),
tmpSpline);
spline[i] = tmpSpline.front();
}
// TODO: Request a GoTools method replacing the above:
// void SplineVolume::computeBasisGrid(double param_u,
// double param_v,
// double param_w,
// BasisPts& result) const
/*
spline.resize(gpar[0].size());
for (size_t i = 0; i < spline.size(); i++)
svol->computeBasis(gpar[0][i],gpar[1][i],gpar[2][i],spline[i]);
*/
}
else
return false;
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
size_t nComp = locSol.size() / this->getNoNodes();
if (nComp*this->getNoNodes() != locSol.size())
return false;
Matrix Xtmp;
Vector Ytmp;
// Evaluate the primary solution field at each point
size_t nPoints = spline.size();
sField.resize(nComp,nPoints);
for (size_t i = 0; i < nPoints; i++)
{
IntVec ip;
scatterInd(n1,n2,n3,p1,p2,p3,spline[i].left_idx,ip);
utl::gather(ip,nComp,locSol,Xtmp);
Xtmp.multiply(spline[i].basisValues,Ytmp);
sField.fillColumn(1+i,Ytmp);
}
return true;
}
bool ASMs3D::evalSolution (Matrix& sField, const Integrand& integrand,
const int* npe, bool project) const
{
if (npe)
{
// Compute parameter values of the result sampling points
RealArray gpar[3];
if (this->getGridParameters(gpar[0],0,npe[0]-1) &&
this->getGridParameters(gpar[1],1,npe[1]-1) &&
this->getGridParameters(gpar[2],2,npe[2]-1))
if (project)
{
// Project the secondary solution onto the spline basis
Go::SplineVolume* v = this->projectSolution(integrand);
if (v)
{
// Evaluate the projected field at the result sampling points
const Vector& svec = sField; // using utl::matrix cast operator
sField.resize(v->dimension(),
gpar[0].size()*gpar[1].size()*gpar[2].size());
v->gridEvaluator(const_cast<Vector&>(svec),gpar[0],gpar[1],gpar[2]);
delete v;
return true;
}
}
else
// Evaluate the secondary solution at all sampling points
return this->evalSolution(sField,integrand,gpar);
}
else
{
// Project the secondary solution onto the spline basis
Go::SplineVolume* v = this->projectSolution(integrand);
if (v)
{
// Extract control point values from the spline object
sField.resize(v->dimension(),
v->numCoefs(0)*v->numCoefs(1)*v->numCoefs(2));
sField.fill(&(*v->coefs_begin()));
delete v;
return true;
}
}
std::cerr <<" *** ASMs3D::evalSolution: Failure!"<< std::endl;
return false;
}
Go::GeomObject* ASMs3D::evalSolution (const Integrand& integrand) const
{
return this->projectSolution(integrand);
}
Go::SplineVolume* ASMs3D::projectSolution (const Integrand& integrand) const
{
// Compute parameter values of the result sampling points
RealArray gpar[3];
for (int dir = 0; dir < 3; dir++)
if (!this->getGrevilleParameters(gpar[dir],dir))
return 0;
// Evaluate the secondary solution at all sampling points
Matrix sValues;
if (!this->evalSolution(sValues,integrand,gpar))
return false;
// Project the results onto the spline basis to find control point
// values based on the result values evaluated at the Greville points.
// Note that we here implicitly assume the the number of Greville points
// equals the number of control points such that we don't have to resize
// the result array. Think that is always the case, but beware if trying
// other projection schemes later.
RealArray weights;
if (svol->rational())
svol->getWeights(weights);
const Vector& vec = sValues;
return Go::VolumeInterpolator::regularInterpolation(svol->basis(0),
svol->basis(1),
svol->basis(2),
gpar[0], gpar[1], gpar[2],
const_cast<Vector&>(vec),
sValues.rows(),
svol->rational(),
weights);
}
bool ASMs3D::evalSolution (Matrix& sField, const Integrand& integrand,
const RealArray* gpar, bool regular) const
{
sField.resize(0,0);
// Evaluate the basis functions and their derivatives at all points
std::vector<Go::BasisDerivs> spline;
if (regular)
{
PROFILE2("Spline evaluation");
svol->computeBasisGrid(gpar[0],gpar[1],gpar[2],spline);
}
else if (gpar[0].size() == gpar[1].size() && gpar[0].size() == gpar[2].size())
{
PROFILE2("Spline evaluation");
spline.resize(gpar[0].size());
std::vector<Go::BasisDerivs> tmpSpline(1);
for (size_t i = 0; i < spline.size(); i++)
{
svol->computeBasisGrid(RealArray(1,gpar[0][i]),
RealArray(1,gpar[1][i]),
RealArray(1,gpar[2][i]),
tmpSpline);
spline[i] = tmpSpline.front();
}
// TODO: Request a GoTools method replacing the above:
// void SplineVolume::computeBasisGrid(double param_u,
// double param_v,
// double param_w,
// BasisDerivs& result) const
/*
spline.resize(gpar[0].size());
for (size_t i = 0; i < spline.size(); i++)
svol->computeBasis(gpar[0][i],gpar[1][i],gpar[2][i],spline[i]);
*/
}
else
return false;
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
// Fetch nodal (control point) coordinates
Matrix Xnod, Xtmp;
this->getNodalCoordinates(Xnod);
Vector N(p1*p2*p3), solPt;
Matrix dNdu, dNdX, Jac;
// Evaluate the secondary solution field at each point
size_t nPoints = spline.size();
for (size_t i = 0; i < nPoints; i++)
{
// Fetch indices of the non-zero basis functions at this point
IntVec ip;
scatterInd(n1,n2,n3,p1,p2,p3,spline[i].left_idx,ip);
// Fetch associated control point coordinates
utl::gather(ip,3,Xnod,Xtmp);
// Fetch basis function derivatives at current integration point
extractBasis(spline[i],N,dNdu);
// Compute the Jacobian inverse
if (utl::Jacobian(Jac,dNdX,Xtmp,dNdu) == 0.0) // Jac = (Xtmp * dNdu)^-1
continue; // skip singular points
// Now evaluate the solution field
if (!integrand.evalSol(solPt,N,dNdX,Xtmp*N,ip))
return false;
else if (sField.empty())
sField.resize(solPt.size(),nPoints,true);
sField.fillColumn(1+i,solPt);
}
return true;
}
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